Subjects -> COMPUTER SCIENCE (Total: 2313 journals)
    - ANIMATION AND SIMULATION (33 journals)
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    - COMPUTER SCIENCE (1305 journals)
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COMPUTER SCIENCE (1305 journals)                  1 2 3 4 5 6 7 | Last

Showing 1 - 200 of 872 Journals sorted alphabetically
3D Printing and Additive Manufacturing     Full-text available via subscription   (Followers: 27)
Abakós     Open Access   (Followers: 3)
ACM Computing Surveys     Hybrid Journal   (Followers: 29)
ACM Inroads     Full-text available via subscription   (Followers: 1)
ACM Journal of Computer Documentation     Free   (Followers: 4)
ACM Journal on Computing and Cultural Heritage     Hybrid Journal   (Followers: 5)
ACM Journal on Emerging Technologies in Computing Systems     Hybrid Journal   (Followers: 11)
ACM SIGACCESS Accessibility and Computing     Free   (Followers: 2)
ACM SIGAPP Applied Computing Review     Full-text available via subscription  
ACM SIGBioinformatics Record     Full-text available via subscription  
ACM SIGEVOlution     Full-text available via subscription  
ACM SIGHIT Record     Full-text available via subscription  
ACM SIGHPC Connect     Full-text available via subscription  
ACM SIGITE Newsletter     Open Access   (Followers: 1)
ACM SIGMIS Database: the DATABASE for Advances in Information Systems     Hybrid Journal  
ACM SIGUCCS plugged in     Full-text available via subscription  
ACM SIGWEB Newsletter     Full-text available via subscription   (Followers: 3)
ACM Transactions on Accessible Computing (TACCESS)     Hybrid Journal   (Followers: 3)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 13)
ACM Transactions on Applied Perception (TAP)     Hybrid Journal   (Followers: 3)
ACM Transactions on Architecture and Code Optimization (TACO)     Hybrid Journal   (Followers: 9)
ACM Transactions on Asian and Low-Resource Language Information Processing (TALLIP)     Hybrid Journal  
ACM Transactions on Autonomous and Adaptive Systems (TAAS)     Hybrid Journal   (Followers: 10)
ACM Transactions on Computation Theory (TOCT)     Hybrid Journal   (Followers: 11)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 5)
ACM Transactions on Computer Systems (TOCS)     Hybrid Journal   (Followers: 19)
ACM Transactions on Computer-Human Interaction     Hybrid Journal   (Followers: 15)
ACM Transactions on Computing Education (TOCE)     Hybrid Journal   (Followers: 9)
ACM Transactions on Computing for Healthcare     Hybrid Journal  
ACM Transactions on Cyber-Physical Systems (TCPS)     Hybrid Journal   (Followers: 1)
ACM Transactions on Design Automation of Electronic Systems (TODAES)     Hybrid Journal   (Followers: 5)
ACM Transactions on Economics and Computation     Hybrid Journal  
ACM Transactions on Embedded Computing Systems (TECS)     Hybrid Journal   (Followers: 4)
ACM Transactions on Information Systems (TOIS)     Hybrid Journal   (Followers: 18)
ACM Transactions on Intelligent Systems and Technology (TIST)     Hybrid Journal   (Followers: 11)
ACM Transactions on Interactive Intelligent Systems (TiiS)     Hybrid Journal   (Followers: 6)
ACM Transactions on Internet of Things     Hybrid Journal   (Followers: 2)
ACM Transactions on Modeling and Performance Evaluation of Computing Systems (ToMPECS)     Hybrid Journal  
ACM Transactions on Multimedia Computing, Communications, and Applications (TOMCCAP)     Hybrid Journal   (Followers: 10)
ACM Transactions on Parallel Computing     Full-text available via subscription  
ACM Transactions on Reconfigurable Technology and Systems (TRETS)     Hybrid Journal   (Followers: 6)
ACM Transactions on Sensor Networks (TOSN)     Hybrid Journal   (Followers: 9)
ACM Transactions on Social Computing     Hybrid Journal  
ACM Transactions on Spatial Algorithms and Systems (TSAS)     Hybrid Journal   (Followers: 1)
ACM Transactions on Speech and Language Processing (TSLP)     Hybrid Journal   (Followers: 11)
ACM Transactions on Storage     Hybrid Journal  
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 39)
Acta Informatica Malaysia     Open Access  
Acta Universitatis Cibiniensis. Technical Series     Open Access   (Followers: 1)
Ad Hoc Networks     Hybrid Journal   (Followers: 12)
Adaptive Behavior     Hybrid Journal   (Followers: 8)
Additive Manufacturing Letters     Open Access   (Followers: 3)
Advanced Engineering Materials     Hybrid Journal   (Followers: 32)
Advanced Science Letters     Full-text available via subscription   (Followers: 9)
Advances in Adaptive Data Analysis     Hybrid Journal   (Followers: 9)
Advances in Artificial Intelligence     Open Access   (Followers: 31)
Advances in Catalysis     Full-text available via subscription   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 20)
Advances in Computer Engineering     Open Access   (Followers: 13)
Advances in Computer Science : an International Journal     Open Access   (Followers: 18)
Advances in Computing     Open Access   (Followers: 3)
Advances in Data Analysis and Classification     Hybrid Journal   (Followers: 52)
Advances in Engineering Software     Hybrid Journal   (Followers: 26)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 19)
Advances in Human-Computer Interaction     Open Access   (Followers: 19)
Advances in Image and Video Processing     Open Access   (Followers: 20)
Advances in Materials Science     Open Access   (Followers: 19)
Advances in Multimedia     Open Access   (Followers: 1)
Advances in Operations Research     Open Access   (Followers: 13)
Advances in Remote Sensing     Open Access   (Followers: 59)
Advances in Science and Research (ASR)     Open Access   (Followers: 8)
Advances in Technology Innovation     Open Access   (Followers: 5)
AEU - International Journal of Electronics and Communications     Hybrid Journal   (Followers: 8)
African Journal of Information and Communication     Open Access   (Followers: 6)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 5)
AI EDAM     Hybrid Journal   (Followers: 2)
Air, Soil & Water Research     Open Access   (Followers: 6)
AIS Transactions on Human-Computer Interaction     Open Access   (Followers: 5)
Al-Qadisiyah Journal for Computer Science and Mathematics     Open Access   (Followers: 2)
AL-Rafidain Journal of Computer Sciences and Mathematics     Open Access   (Followers: 3)
Algebras and Representation Theory     Hybrid Journal  
Algorithms     Open Access   (Followers: 13)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 8)
American Journal of Computational Mathematics     Open Access   (Followers: 6)
American Journal of Information Systems     Open Access   (Followers: 4)
American Journal of Sensor Technology     Open Access   (Followers: 2)
Analog Integrated Circuits and Signal Processing     Hybrid Journal   (Followers: 15)
Animation Practice, Process & Production     Hybrid Journal   (Followers: 4)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 14)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 16)
Annals of Pure and Applied Logic     Open Access   (Followers: 4)
Annals of Software Engineering     Hybrid Journal   (Followers: 12)
Annual Reviews in Control     Hybrid Journal   (Followers: 7)
Anuario Americanista Europeo     Open Access  
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 3)
Applied and Computational Harmonic Analysis     Full-text available via subscription  
Applied Artificial Intelligence: An International Journal     Hybrid Journal   (Followers: 17)
Applied Categorical Structures     Hybrid Journal   (Followers: 4)
Applied Clinical Informatics     Hybrid Journal   (Followers: 4)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 16)
Applied Computer Systems     Open Access   (Followers: 6)
Applied Computing and Geosciences     Open Access   (Followers: 3)
Applied Mathematics and Computation     Hybrid Journal   (Followers: 31)
Applied Medical Informatics     Open Access   (Followers: 11)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 4)
Applied Soft Computing     Hybrid Journal   (Followers: 13)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5)
Applied System Innovation     Open Access   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives and Museum Informatics     Hybrid Journal   (Followers: 97)
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
arq: Architectural Research Quarterly     Hybrid Journal   (Followers: 7)
Array     Open Access   (Followers: 1)
Artifact : Journal of Design Practice     Open Access   (Followers: 8)
Artificial Life     Hybrid Journal   (Followers: 7)
Asian Journal of Computer Science and Information Technology     Open Access   (Followers: 3)
Asian Journal of Control     Hybrid Journal  
Asian Journal of Research in Computer Science     Open Access   (Followers: 4)
Assembly Automation     Hybrid Journal   (Followers: 2)
Automatic Control and Computer Sciences     Hybrid Journal   (Followers: 6)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Automatica     Hybrid Journal   (Followers: 13)
Automatika : Journal for Control, Measurement, Electronics, Computing and Communications     Open Access  
Automation in Construction     Hybrid Journal   (Followers: 8)
Balkan Journal of Electrical and Computer Engineering     Open Access  
Basin Research     Hybrid Journal   (Followers: 7)
Behaviour & Information Technology     Hybrid Journal   (Followers: 32)
BenchCouncil Transactions on Benchmarks, Standards, and Evaluations     Open Access   (Followers: 3)
Big Data and Cognitive Computing     Open Access   (Followers: 5)
Big Data Mining and Analytics     Open Access   (Followers: 10)
Biodiversity Information Science and Standards     Open Access   (Followers: 1)
Bioinformatics     Hybrid Journal   (Followers: 216)
Bioinformatics Advances : Journal of the International Society for Computational Biology     Open Access   (Followers: 1)
Biomedical Engineering     Hybrid Journal   (Followers: 11)
Biomedical Engineering and Computational Biology     Open Access   (Followers: 11)
Briefings in Bioinformatics     Hybrid Journal   (Followers: 43)
British Journal of Educational Technology     Hybrid Journal   (Followers: 93)
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics     Open Access  
c't Magazin fuer Computertechnik     Full-text available via subscription   (Followers: 1)
Cadernos do IME : Série Informática     Open Access  
CALCOLO     Hybrid Journal  
CALICO Journal     Full-text available via subscription  
Calphad     Hybrid Journal  
Canadian Journal of Electrical and Computer Engineering     Full-text available via subscription   (Followers: 14)
Catalysis in Industry     Hybrid Journal  
CCF Transactions on High Performance Computing     Hybrid Journal  
CCF Transactions on Pervasive Computing and Interaction     Hybrid Journal  
CEAS Space Journal     Hybrid Journal   (Followers: 6)
Cell Communication and Signaling     Open Access   (Followers: 3)
Central European Journal of Computer Science     Hybrid Journal   (Followers: 4)
CERN IdeaSquare Journal of Experimental Innovation     Open Access  
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 1)
Chaos, Solitons & Fractals : X     Open Access   (Followers: 1)
Chemometrics and Intelligent Laboratory Systems     Hybrid Journal   (Followers: 13)
ChemSusChem     Hybrid Journal   (Followers: 7)
China Communications     Full-text available via subscription   (Followers: 8)
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chip     Full-text available via subscription   (Followers: 2)
Ciencia     Open Access  
CIN : Computers Informatics Nursing     Hybrid Journal   (Followers: 11)
Circuits and Systems     Open Access   (Followers: 16)
CLEI Electronic Journal     Open Access  
Clin-Alert     Hybrid Journal   (Followers: 1)
Clinical eHealth     Open Access  
Cluster Computing     Hybrid Journal   (Followers: 1)
Cognitive Computation     Hybrid Journal   (Followers: 2)
Cognitive Computation and Systems     Open Access  
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 18)
Communication Methods and Measures     Hybrid Journal   (Followers: 12)
Communication Theory     Hybrid Journal   (Followers: 29)
Communications in Algebra     Hybrid Journal   (Followers: 1)
Communications in Partial Differential Equations     Hybrid Journal   (Followers: 2)
Communications of the ACM     Full-text available via subscription   (Followers: 59)
Communications of the Association for Information Systems     Open Access   (Followers: 15)
Communications on Applied Mathematics and Computation     Hybrid Journal   (Followers: 1)
COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering     Hybrid Journal   (Followers: 4)
Complex & Intelligent Systems     Open Access   (Followers: 1)
Complex Adaptive Systems Modeling     Open Access  
Complex Analysis and Operator Theory     Hybrid Journal   (Followers: 2)
Complexity     Hybrid Journal   (Followers: 8)
Computación y Sistemas     Open Access  
Computation     Open Access   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 3)
Computational and Mathematical Methods     Hybrid Journal  
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 1)
Computational and Structural Biotechnology Journal     Open Access   (Followers: 1)
Computational and Theoretical Chemistry     Hybrid Journal   (Followers: 11)
Computational Astrophysics and Cosmology     Open Access   (Followers: 6)
Computational Biology and Chemistry     Hybrid Journal   (Followers: 13)
Computational Biology Journal     Open Access   (Followers: 6)
Computational Brain & Behavior     Hybrid Journal   (Followers: 1)
Computational Chemistry     Open Access   (Followers: 3)
Computational Communication Research     Open Access   (Followers: 1)
Computational Complexity     Hybrid Journal   (Followers: 5)
Computational Condensed Matter     Open Access   (Followers: 1)

        1 2 3 4 5 6 7 | Last

Similar Journals
Journal Cover
CALCOLO
Journal Prestige (SJR): 0.847
Citation Impact (citeScore): 1
Number of Followers: 0  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 0008-0624 - ISSN (Online) 1126-5434
Published by Springer-Verlag Homepage  [2469 journals]
  • Frequency-explicit approximability estimates for time-harmonic
           Maxwell’s equations

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      Abstract: We consider time-harmonic Maxwell’s equations set in a heterogeneous medium with perfectly conducting boundary conditions. Given a divergence-free right-hand side lying in \(L^2\) , we provide a frequency-explicit approximability estimate measuring the difference between the corresponding solution and its best approximation by high-order Nédélec finite elements. Such an approximability estimate is crucial in both the a priori and a posteriori error analysis of finite element discretizations of Maxwell’s equations, but the derivation is not trivial. Indeed, it is hard to take advantage of high-order polynomials given that the right-hand side only exhibits \(L^2\) regularity. We proceed in line with previously obtained results for the simpler setting of the scalar Helmholtz equation and propose a regularity splitting of the solution. In turn, this splitting yields sharp approximability estimates generalizing known results for the scalar Helmholtz equation and showing the interest of high-order methods.
      PubDate: 2022-05-16
       
  • Correction to: A self-adaptive three-term conjugate gradient method for
           monotone nonlinear equations with convex constraints

    • Free pre-print version: Loading...

      PubDate: 2022-05-14
       
  • Improved CRI iteration methods for a class of complex symmetric linear
           systems

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      Abstract: For solving a class of complex symmetric linear systems, we improve the combination method of real part and imaginary part (CRI) by introducing two optimization techniques—minimum residual and block successive overrelaxation acceleration—and obtain two new iteration methods: minimum residual CRI (MRCRI) and modified CRI (MCRI). Theoretical analysis implies that the new methods are convergent under suitable conditions. Numerical experiments are used to confirm the effectiveness of the MRCRI and MCRI methods, and experiments of parameter sensitivity show that the MRCRI method is more effective than the CRI and PMHSS methods.
      PubDate: 2022-05-05
       
  • Componentwise perturbation analysis for the generalized Schur
           decomposition

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      Abstract: Abstract By defining two important terms called basic perturbation vectors and obtaining their linear bounds, we obtain the linear componentwise perturbation bounds for unitary factors and upper triangular factors of the generalized Schur decomposition. The perturbation bounds for the diagonal elements of the upper triangular factors and the generalized invariant subspace are also derived. From the former, we present an upper bound and a condition number of the generalized eigenvalue. Furthermore, with numerical iterative method, the nonlinear componentwise perturbation bounds of the generalized Schur decomposition are also provided. Numerical examples are given to test the obtained bounds. Among them, we compare our upper bound and condition number of the generalized eigenvalue with their counterparts given in the literature. Numerical results show that they are very close to each other but our results don’t contain the information on the left and right generalized eigenvectors.
      PubDate: 2022-04-20
       
  • Virtual element analysis of nonlocal coupled parabolic problems on
           polygonal meshes

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      Abstract: Abstract In this article, we consider the discretization of nonlocal coupled parabolic problem within the framework of the virtual element method. The presence of nonlocal coefficients not only makes the computation of the Jacobian more expensive in Newton’s method, but also destroys the sparsity of the Jacobian. In order to resolve this problem, an equivalent formulation that has very simple Jacobian is proposed. We derive the error estimates in the \(L^2\) and \(H^1\) norms. To further reduce the computational complexity, a linearized scheme without compromising the rate of convergence in different norms is proposed. Finally, the theoretical results are justified through numerical experiments over arbitrary polygonal meshes.
      PubDate: 2022-03-17
       
  • Composite symmetric second derivative general linear methods for
           Hamiltonian systems

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      Abstract: Abstract Symmetric second derivative general linear methods (SGLMs) have been already introduced for the numerical solution of time-reversible differential equations. To construct suitable high order methods for such problems, the newly developed composition theory has been successfully used for structure-preserving methods. In this paper, composite symmetric SGLMs are introduced using the generalization of composite theory for general linear methods. Then, we construct symmetric methods of order six by the composition of symmetric SGLMs of order four. Numerical results of the constructed methods verify the theoretical order of accuracy and illustrate that the invariants of motion over long time intervals for reversible Hamiltonian systems are well preserved.
      PubDate: 2022-03-14
       
  • Accelerated memory-less SR1 method with generalized secant equation for
           unconstrained optimization

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      Abstract: Abstract The memory-less SR1 with generalized secant equation (MM-SR1gen) is presented and developed together with its numerical performances for solving a collection of 800 unconstrained optimization problems with the number of variables in the range [1000, 10000]. The convergence of the MM-SR1gen method is proved under the classical assumptions. Comparison between the MM-SR1gen versus the memory-less SR1 method, versus the memory-less BFGS method and versus the BFGS in implementation of Shanno and Phua from CONMIN show that MM-SR1gen is more efficient and more robust than these algorithms. By solving five applications from MINPACK-2 collection, each of them with 40,000 variables, we have the computational evidence that MM-SR1gen is more efficient than memory-less SR1 and than memory-less BFGS. The conclusion of this study is that the memory-less SR1 method with generalized secant equation is a rapid and reliable method for solving large-scale minimizing problems. Besides, it is shown that the accuracy of the Hessian approximations along the iterations in quasi-Newton methods is not as crucial in these methods as it is believed.
      PubDate: 2022-03-11
       
  • Efficient iteration methods for complex systems with an indefinite matrix
           term

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      Abstract: Abstract Complex valued systems with an indefinite matrix term arise in important applications such as for certain time-harmonic partial differential equations such as the Maxwell’s equation and for the Helmholtz equation. Complex systems with symmetric positive definite matrices can be solved readily by rewriting the complex matrix system in two-by-two block matrix form with real matrices which can be efficiently solved by iteration using the preconditioned square block (PRESB) preconditioning method and preferably accelerated by the Chebyshev method. The appearances of an indefinite matrix term causes however some difficulties. To handle this we propose different forms of matrix splitting methods, with or without any parameters involved. A matrix spectral analyses is presented followed by extensive numerical comparisons of various forms of the methods.
      PubDate: 2022-03-10
       
  • Optimal three-stage implicit exponentially-fitted RKN methods for solving
           second-order ODEs

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      Abstract: Abstract In a wide range of applications, second-order ordinary differential equation (ODE) appears frequently. If the second-order ODE is stiff, the implicit Runge–Kutta–Nyström (RKN) method is often used to obtain numerical solutions. In addition, there are often some inherent properties in these problems, such as symmetry, symplecticness and exponentially fitting. Considering these properties, two three-stage implicit modified RKN integrators are obtained in this paper. The new six-order integrators called ISSEFMRKN integrate exactly differential systems whose solutions can be expressed as linear combinations of functions from the set \(\{\exp (\lambda t), \exp (-\lambda t)\mid \lambda \in \mathbb {R}~\text {or}~\lambda \in \mathbb {C}\}\) . Furthermore, their final stages are also exact for \(y=t^2\) or \(y\in \{\exp (2\lambda t), \exp (-2\lambda t)\}\) . The numerical results show that the new methods are more accurate than some highly accurate codes in the literature.
      PubDate: 2022-03-02
      DOI: 10.1007/s10092-022-00456-7
       
  • Randomised one-step time integration methods for deterministic operator
           differential equations

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      Abstract: Abstract Uncertainty quantification plays an important role in problems that involve inferring a parameter of an initial value problem from observations of the solution. Conrad et al. (Stat Comput 27(4):1065–1082, 2017) proposed randomisation of deterministic time integration methods as a strategy for quantifying uncertainty due to the unknown time discretisation error. We consider this strategy for systems that are described by deterministic, possibly time-dependent operator differential equations defined on a Banach space or a Gelfand triple. Our main results are strong error bounds on the random trajectories measured in Orlicz norms, proven under a weaker assumption on the local truncation error of the underlying deterministic time integration method. Our analysis establishes the theoretical validity of randomised time integration for differential equations in infinite-dimensional settings.
      PubDate: 2022-02-25
      DOI: 10.1007/s10092-022-00457-6
       
  • Correction to: Analysis of generalised alternating local discontinuous
           Galerkin method on layer-adapted mesh for singularly perturbed problems

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      PubDate: 2022-02-07
      DOI: 10.1007/s10092-022-00455-8
       
  • Efficient and accurate computation for the $$\varphi$$ φ -functions
           arising from exponential integrators

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      Abstract: Abstract In this paper, we develop efficient and accurate algorithms for evaluating both \(\varphi _l(A)\) and \(\varphi _l(A)b,\) where \(\varphi _l(\cdot )\) is the function related to the exponential defined by \(\varphi _l(z)\equiv \sum \nolimits ^{\infty }_{k=0}\frac{z^k}{(l+k)!}\) , A is an \(N\times N\) matrix and b is an N dimensional vector. Such matrix functions play a key role in a class of numerical methods well-known as exponential integrators. The algorithms use the modified scaling and squaring procedure combined with truncated Taylor series. A quasi-backward error analysis is presented to find the optimal value of the scaling and the degree of the Taylor approximation. Some useful techniques are employed for reducing the computational cost. Numerical comparisons with state-of-the-art algorithms show that the algorithms perform well in both accuracy and efficiency.
      PubDate: 2022-01-21
      DOI: 10.1007/s10092-021-00453-2
       
  • Rational interpolation operator with finite Lebesgue constant

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      Abstract: Abstract Classical rational interpolation usually enjoys better approximation properties than polynomial interpolation because it avoids wild oscillations and exhibits exponential convergence for approximating analytic functions. We develop a rational interpolation operator, which not only preserves the advantage of classical rational interpolation, but also has a finite Lebesgue constant. In particular, it is convergent for approximating any continuous function, and the convergence rate of the interpolants approximating a function is obtained using the modulus of continuity.
      PubDate: 2022-01-17
      DOI: 10.1007/s10092-021-00454-1
       
  • A mass and energy conservative fourth-order compact difference scheme for
           the Klein-Gordon-Dirac equations $$^{\star }$$ ⋆

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      Abstract: Abstract This paper is concerned with numerical solution of the two-dimensional Klein-Gordon-Dirac equations by a fourth-order compact finite difference method in space and an energy-preserving Crank-Nicolson-type discretization in time. For convenience of illustrating the conservative properties and investigating the convergence results, we convert the component-wise form of the proposed scheme into an equivalent matrix-vector form. By using the mathematical induction argument and standard energy method, we establish the optimal error estimates under condition \(\tau \le \frac{1}{ \mathrm {ln}(h) }\) with time step \(\tau\) and mesh size h. Compared with the condition \(\tau =O(h^{\frac{1}{2}})\) required by existing results in literature for two-dimensional case, this greatly relaxes the dependence of the time step on the grid size. The convergence order of the scalar \(\phi\) and the 2-spinor \(\psi\) is of \(O(\tau ^{2}+h^{4})\) in the maximum norm and the discrete \(H^{1}\) -norm, respectively. In addition, by using the orthogonal diagonalization technique, a fast solver is designed to solve the proposed scheme. Several numerical results are reported to verify the error estimates and the discrete conservation laws.
      PubDate: 2021-12-21
      DOI: 10.1007/s10092-021-00452-3
       
  • Local minimizers of the Crouzeix ratio: a nonsmooth optimization case
           study

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      Abstract: Abstract Given a square matrix A and a polynomial p, the Crouzeix ratio is the norm of the polynomial on the field of values of A divided by the 2-norm of the matrix p(A). Crouzeix’s conjecture states that the globally minimal value of the Crouzeix ratio is 0.5, regardless of the matrix order and polynomial degree, and it is known that 1 is a frequently occurring locally minimal value. Making use of a heavy-tailed distribution to initialize our optimization computations, we demonstrate for the first time that the Crouzeix ratio has many other locally minimal values between 0.5 and 1. Besides showing that the same function values are repeatedly obtained for many different starting points, we also verify that an approximate nonsmooth stationarity condition holds at computed candidate local minimizers. We also find that the same locally minimal values are often obtained both when optimizing over real matrices and polynomials, and over complex matrices and polynomials. We argue that minimization of the Crouzeix ratio makes a very interesting nonsmooth optimization case study, illustrating among other things how effective the BFGS method is for nonsmooth, nonconvex optimization. Our method for verifying approximate nonsmooth stationarity is based on what may be a novel approach to finding approximate subgradients of max functions on an interval. Our extensive computations strongly support Crouzeix’s conjecture: in all cases, we find that the smallest locally minimal value is 0.5.
      PubDate: 2021-12-18
      DOI: 10.1007/s10092-021-00448-z
       
  • PVTSI $$^{{{(m)}}}$$ ( m ) : A novel approach to computation of Hadamard
           finite parts of nonperiodic singular integrals

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      Abstract: Abstract We consider the numerical computation of \(I[f]=\int \!\!\!\!\!=^b_a f(x)\,dx\) , the Hadamard finite part of the finite-range singular integral \(\int ^b_a f(x)\,dx\) , \(f(x)=g(x)/(x-t)^{m}\) with \(a<t<b\) and \(m\in \{1,2,\ldots \},\) assuming that (i)  \(g\in C^\infty (a,b)\) and (ii) g(x) is allowed to have arbitrary integrable singularities at the endpoints \(x=a\) and \(x=b\) . We first prove that \(\int \!\!\!\!\!=^b_a f(x)\,dx\) is invariant under any legitimate variable transformation \(x=\psi (\xi )\) , \(\psi :[\alpha ,\beta ]\rightarrow [a,b]\) , hence there holds \(\int \!\!\!\!\!=^\beta _\alpha F(\xi )\,d\xi =\int \!\!\!\!\!=^b_a f(x)\,dx\) , where \(F(\xi )=f(\psi (\xi ))\,\psi '(\xi )\) . Based on this result, we next choose \(\psi (\xi )\) such that \(\mathcal{{F}}(\xi )\) , the \({{\mathcal {T}}}\) -periodic extension of \(F(\xi )\) , \({{\mathcal {T}}}=\beta -\alpha \) , is sufficiently smooth, and prove, with the help of some recent extension/generalization of the Euler–Maclaurin expansion, that we can apply to \(\int \!\!\!\!\!=^\beta _\alpha F(\xi )\,d\xi \) the quadrature formulas derived for periodic singular integrals developed in an earlier work of the author: [A. Sidi, “Unified compact numerical quadrature formulas for Hadamard finite parts of singular integrals of periodic functions.” Calcolo, 58, 2021. Article number 22]. We give a whole family of numerical quadrature formulas for \(\int \!\!\!\!\!=^\beta _\alpha F(\xi )\,d\xi \) for each m, which we denote \({\widehat{T}}^{(s)}_{m,n}[\mathcal{{F}}]\) . Letting \(G(\xi )=(\xi -\tau )^m F(\xi )\) , with \(\tau \in (\alpha ,\beta )\) determined from \(t=\psi (\tau )\) , and letting \(h={\mathcal {T}}/n\) , for \(m=3\) , for example, we have the three formulas $$\begin{aligned} {\widehat{T}}^{(0)}_{3,n}[\mathcal{{F}}]&=h\sum ^{n-1}_{j=1}\mathcal{{F}}(\tau +jh)-\frac{\pi ^2}{3}\,G'(\tau )\,h^{-1} +\frac{1}{6}\,...
      PubDate: 2021-12-18
      DOI: 10.1007/s10092-021-00446-1
       
  • A new non-augmented and momentum-conserving fully-mixed finite element
           method for a coupled flow-transport problem

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      Abstract: Abstract We propose and analyze a new mixed finite element method for the coupling of the Stokes equations with a transport problem modelled by a scalar nonlinear convection–diffusion problem. Our approach is based on the introduction of the Cauchy fluid stress and two vector unknowns involving the gradient and the total flux of the concentration. The introduction of these further unknowns lead to a mixed formulation in a Banach space framework in both Stokes and transport equations, where the aforementioned stress tensor and vector unknowns, together with the velocity and the concentration, are the main unknowns of the system. In this way, and differently from the techniques previously developed for this and related coupled problems, no augmentation procedure needs to be incorporated now into the formulation nor into the solvability analysis. The resulting non-augmented scheme is then written equivalently as a fixed-point equation, so that the well-known Banach theorem, combined with Babuška–Brezzi’s theory in Banach spaces, classical results on nonlinear monotone operators and certain regularity assumptions, are applied to prove the unique solvability of the continuous system. As for the associated Galerkin scheme, whose solvability is established similarly to the continuous case by using the Brouwer fixed-point theorem, we employ Raviart–Thomas approximations of order \(k \ge 0\) for the stress and total flux, and discontinuous piecewise polynomials of degree k for the velocity, concentration, and concentration gradient. With this choice of spaces, momentum is conserved in both Stokes and transport equations if the external forces belong to the piecewise constants and concentration discrete space, respectively, which constitutes one of the main features of our approach. Finally, we derive optimal a priori error estimates and provide several numerical results illustrating the good performance of the scheme and confirming the theoretical rates of convergence.
      PubDate: 2021-12-11
      DOI: 10.1007/s10092-021-00451-4
       
  • A lowest-degree quasi-conforming finite element de Rham complex on general
           quadrilateral grids by piecewise polynomials

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      Abstract: Abstract This paper discusses finite elements defined by Ciarlet’s triple on grids that consist of general quadrilaterals not limited in parallelograms. Specifically, two finite elements are established for the \(H^1\) and \(H(\mathrm rot)\) elliptic problems, respectively. An \({\mathcal {O}}(h)\) order convergence rate in energy norm for both of them and an \({\mathcal {O}}(h^2)\) order convergence in \(L^2\) norm for the \(H^1\) scheme are proved under the \({\mathcal {O}}(h^2)\) asymptotic-parallelogram assumption on the grids. Further, these two finite element spaces, together with the space of piecewise constant functions, formulate a discretized de Rham complex on general quadrilateral grids. The finite element spaces consist of piecewise polynomial functions, and, thus, are nonconforming on general quadrilateral grids. Indeed, a rigorous analysis is given in this paper that it is impossible to construct a practically useful finite element by Ciarlet’s triple that can formulate a finite element space which consists of continuous piecewise polynomial functions on a grid that may include arbitrary quadrilaterals.
      PubDate: 2021-12-07
      DOI: 10.1007/s10092-021-00447-0
       
  • On the convergence rate of the Kačanov scheme for shear-thinning
           fluids

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      Abstract: Abstract We explore the convergence rate of the Kačanov iteration scheme for different models of shear-thinning fluids, including Carreau and power-law type explicit quasi-Newtonian constitutive laws. It is shown that the energy difference contracts along the sequence generated by the iteration. In addition, an a posteriori computable contraction factor is proposed, which improves, on finite-dimensional Galerkin spaces, previously derived bounds on the contraction factor in the context of the power-law model. Significantly, this factor is shown to be independent of the choice of the cut-off parameters whose use was proposed in the literature for the Kačanov iteration applied to the power-law model. Our analytical findings are confirmed by a series of numerical experiments.
      PubDate: 2021-11-28
      DOI: 10.1007/s10092-021-00444-3
       
  • A proximal point like method for solving tensor least-squares problems

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      Abstract: Abstract The goal of this paper is to solve the tensor least-squares (TLS) problem associated with multilinear system \(\mathcal {A}{} \mathbf{x} ^{m-1}=\mathbf{b}\) , where \(\mathcal {A}\) is an mth-order n-dimensional tensor and \(\mathbf{b}\) is a vector in \(\mathbb {R}^{n}\) , which has practical applications in numerical PDEs, data mining, tensor complementary problems, higher order statistics and so on. We transform the TLS problem into a multi-block optimization problem with consensus constraints, and propose an alternating linearized method with proximal regularization for it. Under some mild assumptions, it is shown that every limit point of the sequence generated by this method is a stationary point. Moreover, when the tensor \(\mathcal {A}\) can be constructed in the tensor-train format explicitly, the total number of operations with respect to the method mentioned above decreases from the order of \(\mathcal {O}(n^{m-1})\) to \(\mathcal {O}((m-1)^2nr^2)+\mathcal {O}(mnr^3)\) , alleviating the curse-of-dimensionality. As an application, the inverse iteration methods, derived from the proposed methods, for solving the tensor eigenvalue problems are presented. Some numerical examples are provided to illustrate the feasibility of our algorithms.
      PubDate: 2021-11-26
      DOI: 10.1007/s10092-021-00450-5
       
 
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