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  Subjects -> MATHEMATICS (Total: 968 journals)
    - APPLIED MATHEMATICS (81 journals)
    - GEOMETRY AND TOPOLOGY (20 journals)
    - MATHEMATICS (714 journals)
    - MATHEMATICS (GENERAL) (41 journals)
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    - PROBABILITIES AND MATH STATISTICS (90 journals)

MATHEMATICS (714 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 4)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 15)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 31)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 12)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 10)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 4)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 4)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 19)
Advances in Decision Sciences     Open Access   (Followers: 3)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 14)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 3)
Advances in Materials Science     Open Access   (Followers: 14)
Advances in Mathematical Physics     Open Access   (Followers: 4)
Advances in Mathematics     Full-text available via subscription   (Followers: 11)
Advances in Numerical Analysis     Open Access   (Followers: 5)
Advances in Operations Research     Open Access   (Followers: 12)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 6)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 12)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 6)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 5)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 6)
American Journal of Operations Research     Open Access   (Followers: 5)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 9)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 5)
Analysis Mathematica     Full-text available via subscription  
Analysis. International mathematical journal of analysis and its applications     Hybrid Journal   (Followers: 2)
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 4)
Annals of Data Science     Hybrid Journal   (Followers: 12)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription   (Followers: 1)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
Annals of Pure and Applied Logic     Open Access   (Followers: 3)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 2)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 7)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 8)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 2)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 21)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 6)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 4)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 1)
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 20)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 12)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 2)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 4)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 19)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 1)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 14)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 2)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 8)
Compositio Mathematica     Full-text available via subscription   (Followers: 1)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 8)
Concrete Operators     Open Access   (Followers: 5)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 13)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 9)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 30)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 3)
Differentsial'nye Uravneniya     Open Access  
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Eco Matemático     Open Access  
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Combinatorics     Open Access  
Electronic Journal of Differential Equations     Open Access  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 4)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)

        1 2 3 4 | Last

Journal Cover
Advances in Computational Mathematics
Journal Prestige (SJR): 0.812
Citation Impact (citeScore): 1
Number of Followers: 19  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1572-9044 - ISSN (Online) 1019-7168
Published by Springer-Verlag Homepage  [2350 journals]
  • Multivariate exponential analysis from the minimal number of samples
    • Authors: Annie Cuyt; Wen-shin Lee
      Pages: 987 - 1002
      Abstract: The problem of multivariate exponential analysis or sparse interpolation has received a lot of attention, especially with respect to the number of samples required to solve it unambiguously. In this paper we show how to bring the number of samples down to the absolute minimum of (d + 1)n where d is the dimension of the problem and n is the number of exponential terms. To this end we present a fundamentally different approach for the multivariate problem statement. We combine a one-dimensional exponential analysis method such as ESPRIT, MUSIC, the matrix pencil or any Prony-like method, with some linear systems of equations because the multivariate exponents are inner products and thus linear expressions in the parameters.
      PubDate: 2018-08-01
      DOI: 10.1007/s10444-017-9570-8
      Issue No: Vol. 44, No. 4 (2018)
       
  • Morley-Wang-Xu element methods with penalty for a fourth order elliptic
           singular perturbation problem
    • Authors: Wenqing Wang; Xuehai Huang; Kai Tang; Ruiyue Zhou
      Pages: 1041 - 1061
      Abstract: Two Morley-Wang-Xu element methods with penalty for the fourth order elliptic singular perturbation problem are proposed in this paper, including the interior penalty Morley-Wang-Xu element method and the super penalty Morley-Wang-Xu element method. The key idea in designing these two methods is combining the Morley-Wang-Xu element and penalty formulation for the Laplace operator. Robust a priori error estimates are derived under minimal regularity assumptions on the exact solution by means of some established a posteriori error estimates. Finally, we present some numerical results to demonstrate the theoretical estimates.
      PubDate: 2018-08-01
      DOI: 10.1007/s10444-017-9572-6
      Issue No: Vol. 44, No. 4 (2018)
       
  • A partially isochronous splitting algorithm for three-block separable
           convex minimization problems
    • Authors: Hongjin He; Liusheng Hou; Hong-Kun Xu
      Pages: 1091 - 1115
      Abstract: During the last decade, the state-of-the-art alternating direction method of multipliers (ADMM) has successfully been used to solve many two-block separable convex minimization problems arising from several applied areas such as signal/image processing and statistical and machine learning. It however remains an interesting problem of how to implement ADMM to three-block separable convex minimization problems as required by the situation where many objective functions in the above-mentioned areas are actually more conveniently decomposed to the sum of three convex functions, due also to the observation that the straightforward extension of ADMM from the two-block case to the three-block case is apparently not convergent. In this paper, we shall introduce a new algorithm that is called a partially isochronous splitting algorithm (PISA) in order to implement ADMM for the three-block separable model. The main idea of our algorithm is to incorporate only one proximal term into the last subproblem of the extended ADMM so that the resulting algorithm maximally inherits the promising properties of ADMM. A remarkable superiority over the extended ADMM is that we can simultaneously solve two of the subproblems, thereby taking advantages of the separable structure and parallel architectures. Theoretically, we will establish the global convergence of our algorithm under standard conditions, and also the O(1/t) rate of convergence in both ergodic and nonergodic senses, where t is the iteration counter. The computational competitiveness of our algorithm is shown by numerical experiments on an application to the well-tested robust principal component analysis model.
      PubDate: 2018-08-01
      DOI: 10.1007/s10444-017-9574-4
      Issue No: Vol. 44, No. 4 (2018)
       
  • Correction to: A partially isochronous splitting algorithm for three-block
           separable convex minimization problems
    • Authors: Hongjin He; Liusheng Hou; Hong-Kun Xu
      Pages: 1117 - 1118
      Abstract: The original publication of this article has an error.
      PubDate: 2018-08-01
      DOI: 10.1007/s10444-018-9591-y
      Issue No: Vol. 44, No. 4 (2018)
       
  • Nonlinear approximation with nonstationary Gabor frames
    • Authors: Emil Solsbæk Ottosen; Morten Nielsen
      Pages: 1183 - 1203
      Abstract: We consider sparseness properties of adaptive time-frequency representations obtained using nonstationary Gabor frames (NSGFs). NSGFs generalize classical Gabor frames by allowing for adaptivity in either time or frequency. It is known that the concept of painless nonorthogonal expansions generalizes to the nonstationary case, providing perfect reconstruction and an FFT based implementation for compactly supported window functions sampled at a certain density. It is also known that for some signal classes, NSGFs with flexible time resolution tend to provide sparser expansions than can be obtained with classical Gabor frames. In this article we show, for the continuous case, that sparseness of a nonstationary Gabor expansion is equivalent to smoothness in an associated decomposition space. In this way we characterize signals with sparse expansions relative to NSGFs with flexible time resolution. Based on this characterization we prove an upper bound on the approximation error occurring when thresholding the coefficients of the corresponding frame expansions. We complement the theoretical results with numerical experiments, estimating the rate of approximation obtained from thresholding the coefficients of both stationary and nonstationary Gabor expansions.
      PubDate: 2018-08-01
      DOI: 10.1007/s10444-017-9577-1
      Issue No: Vol. 44, No. 4 (2018)
       
  • A numerical method for solving the time fractional Schrödinger
           equation
    • Authors: Na Liu; Wei Jiang
      Pages: 1235 - 1248
      Abstract: In this article, we proposed a new numerical method to obtain the approximation solution for the time-fractional Schrödinger equation based on reproducing kernel theory and collocation method. In order to overcome the weak singularity of typical solutions, we apply the integral operator to both sides of differential equation and yield a integral equation. We divided the solution of this kind equation into two parts: imaginary part and real part, and then derived the approximate solutions of the two parts in the form of series with easily computable terms in the reproducing kernel space. New bases of reproducing kernel spaces are constructed and the existence of approximate solution is proved. Numerical examples are given to show the accuracy and effectiveness of our approach.
      PubDate: 2018-08-01
      DOI: 10.1007/s10444-017-9579-z
      Issue No: Vol. 44, No. 4 (2018)
       
  • A boundary integral equation method for mode elimination and vibration
           confinement in thin plates with clamped points
    • Authors: Alan E. Lindsay; Bryan Quaife; Laura Wendelberger
      Pages: 1249 - 1273
      Abstract: We consider the bi-Laplacian eigenvalue problem for the modes of vibration of a thin elastic plate with a discrete set of clamped points. A high-order boundary integral equation method is developed for efficient numerical determination of these modes in the presence of multiple localized defects for a wide range of two-dimensional geometries. The defects result in eigenfunctions with a weak singularity that is resolved by decomposing the solution as a superposition of Green’s functions plus a smooth regular part. This method is applied to a variety of regular and irregular domains and two key phenomena are observed. First, careful placement of clamping points can entirely eliminate particular eigenvalues and suggests a strategy for manipulating the vibrational characteristics of rigid bodies so that undesirable frequencies are removed. Second, clamping of the plate can result in partitioning of the domain so that vibrational modes are largely confined to certain spatial regions. This numerical method gives a precision tool for tuning the vibrational characteristics of thin elastic plates.
      PubDate: 2018-08-01
      DOI: 10.1007/s10444-017-9580-6
      Issue No: Vol. 44, No. 4 (2018)
       
  • Fast elliptic curve point multiplication based on binary and binary
           non-adjacent scalar form methods
    • Authors: Denis Khleborodov
      Pages: 1275 - 1293
      Abstract: This article presents two methods for developing algorithms of computing scalar multiplication in groups of points on an elliptic curve over finite fields. Two new effective algorithms have been presented: one of them is based on a binary Non-Adjacent Form of scalar representation and another one on a binary of scalar representation method. All algorithms were developed based on simple and composite operations with point and also based on affine and Jacobi coordinates systems taking into account the latest achievements in computing cost reduction. Theorems concerning their computational complexity are formulated and proved for these new algorithms. In the end of this article comparative analysis of both new algorithms among themselves and previously known algorithms are represented.
      PubDate: 2018-08-01
      DOI: 10.1007/s10444-017-9581-5
      Issue No: Vol. 44, No. 4 (2018)
       
  • A note on “Reguralizers for structured sparsity”
    • Authors: F. Lara
      Pages: 1321 - 1323
      Abstract: In this note, the notion of admissible sets contained in the strictly positive orthant introduced in Micchelli et al. (Adv. Comp. Math. 38(3), 455–489 2013) is analyzed. This notion was used to generalize theoretical results and optimization methods for structured sparsity. Unfortunately, we will prove that there is no generalization using admissible sets.
      PubDate: 2018-08-01
      DOI: 10.1007/s10444-017-9583-3
      Issue No: Vol. 44, No. 4 (2018)
       
  • An accurate spectral method for the transverse magnetic mode of Maxwell
           equations in Cole-Cole dispersive media
    • Authors: Can Huang; Li-Lian Wang
      Abstract: In this paper, we propose an accurate numerical means built upon a spectral-Galerkin method in spatial discretization and an enriched multi-step spectral-collocation approach in temporal direction, for the transverse magnetic mode of Maxwell equations in Cole-Cole dispersive media in two-dimensional setting. Our starting point is to derive a new model involving only one unknown field from the original model with three unknown fields: electric, magnetic fields, and the induced electric polarization (described by a global temporal convolution of the electric field). This results in a second-order integral-differential equation with a weakly singular integral kernel expressed by the Mittag-Lefler (ML) function. The most interesting but challenging issue resides in how to efficiently deal with the singularity in time induced by the ML function which is an infinite series of singular power functions with different nature. With this in mind, we introduce a spectral-Galerkin method using Fourier-like basis functions for spatial discretization, leading to a sequence of decoupled temporal integral-differential equations (IDE) with the same weakly singular kernel involving the ML function as the original two-dimensional problem. With a careful study of the regularity of IDE, we incorporate several leading singular terms into the numerical scheme and approximate much regular part of the solution. Then, we solve the IDE by a multi-step well-conditioned collocation scheme together with mapping technique to increase the accuracy and enhance the resolution. We show that such an enriched collocation method is convergent and accurate.
      PubDate: 2018-09-20
      DOI: 10.1007/s10444-018-9636-2
       
  • Higher order analysis of the geometry of singularities using the Taylorlet
           transform
    • Authors: Thomas Fink
      Abstract: We consider an extension of the continuous shearlet transform which additionally uses higher order shears. This extension, called the Taylorlet transform, allows for a detection of the position, the orientation, the curvature, and other higher order geometric information of singularities. Employing the novel vanishing moment conditions of higher order, \({\int }_{\mathbb {R}} g(\pm t^{k})t^{m} dt= 0\) for \(k,m\in \mathbb {N}\) , k ≥ 1, on the analyzing function \(g\in \mathcal {S}(\mathbb {R})\) , we can show that the Taylorlet transform exhibits different decay rates for decreasing scales depending on the choice of the higher order shearing variables. This enables a faster detection of the geometric information of singularities in terms of the decay rate with respect to the dilation parameter. Furthermore, we present a construction that yields analyzing functions which fulfill vanishing moment conditions of different orders simultaneously.
      PubDate: 2018-09-18
      DOI: 10.1007/s10444-018-9635-3
       
  • Correction to: Nonlocal operators with local boundary conditions in higher
           dimensions
    • Authors: Burak Aksoylu; Fatih Celiker; Orsan Kilicer
      Abstract: In the original publication, Figure 4 image should be Figure 5, Figure 5 image was a repetition of Figure 6 and the correct image of Figure 4 was not shown. The original article was updated by correcting the images of figures 4, 5, and 6.
      PubDate: 2018-09-14
      DOI: 10.1007/s10444-018-9632-6
       
  • Extensions of planar GC sets and syzygy matrices
    • Authors: Jesús M. Carnicer; Carmen Godés
      Abstract: The geometric characterization, introduced by Chung and Yao, identifies node sets for total degree interpolation such that the Lagrange fundamental polynomials are products of linear factors. Sets satisfying the geometric characterization are usually called GC sets. Gasca and Maeztu conjectured that planar GC sets of degree n contain n + 1 collinear points. It has been shown that the conjecture holds for degrees not greater than 5 but it is still unsolved for general degree. One promising approach consists of studying the syzygies of the ideal of polynomials vanishing at the nodes. In order to describe syzygy matrices of GC sets, we analyze the extension of a GC set of degree n to a GC set of degree n + 1, by adding a n + 2 nodes on a line.
      PubDate: 2018-09-13
      DOI: 10.1007/s10444-018-9630-8
       
  • New integer-order approximations of discrete-time non-commensurate
           fractional-order systems using the cross Gramian
    • Authors: Marek Rydel
      Abstract: This paper presents a new approach to modeling of linear time-invariant discrete-time non-commensurate fractional-order single-input single-output state space systems by means of the Balanced Truncation and Frequency Weighted model order reduction methods based on the cross Gramian. These reduction methods are applied to the specific rational (integer-order) FIR-based approximation to the fractional-order system, which enables to introduce simple, analytical formulae for determination of the cross Gramian of the system. This leads to significant decrease of computational burden in the reduction algorithm. As a result, a rational and relatively low-order state space approximator for the fractional-order system is obtained. A simulation experiment illustrates an efficiency of the introduced methodology in terms of high approximation accuracy and low time complexity of the proposed method.
      PubDate: 2018-09-08
      DOI: 10.1007/s10444-018-9633-5
       
  • Two-grid finite element methods combined with Crank-Nicolson scheme for
           nonlinear Sobolev equations
    • Authors: Chuanjun Chen; Kang Li; Yanping Chen; Yunqing Huang
      Abstract: In this paper, we present a second-order accurate Crank-Nicolson scheme for the two-grid finite element methods of the nonlinear Sobolev equations. This method involves solving a small nonlinear system on a coarse mesh with mesh size H and a linear system on a fine mesh with mesh size h, which can still maintain the asymptotically optimal accuracy compared with the standard finite element method. However, the two-grid scheme can reduce workload and save a lot of CPU time. The optimal error estimates in H1-norm show that the two-grid methods can achieve optimal convergence order when the mesh sizes satisfy h = O(H2). These estimates are shown to be uniform in time. Numerical results are provided to verify the theoretical estimates.
      PubDate: 2018-08-31
      DOI: 10.1007/s10444-018-9628-2
       
  • On the discontinuity of images recovered by noncovex nonsmooth regularized
           isotropic models with box constraints
    • Authors: Chao Zeng; Chunlin Wu
      Abstract: Nonconvex nonsmooth regularizations have exhibited the ability of restoring images with neat edges in many applications, which has been provided a mathematical explanation by analyzing the discontinuity of the local minimizers of the variational models. Since in many applications the pixel intensity values in digital images are restricted in a certain given range, box constraints are adopted to improve the restorations. A similar property of nonconvex nonsmooth regularization for box-constrained models has been proved in the literature. While many theoretical results are available for anisotropic models, we investigate the isotropic case. We establish similar theoretical results for isotropic nonconvex nonsmooth models with box constraints. Numerical experiments are presented to validate our theoretical results.
      PubDate: 2018-08-21
      DOI: 10.1007/s10444-018-9629-1
       
  • A non-convex regularization approach for compressive sensing
    • Authors: Ya-Ru Fan; Alessandro Buccini; Marco Donatelli; Ting-Zhu Huang
      Abstract: Compressive sensing (CS) aims at reconstructing high dimensional data from a small number of samples or measurements. In this paper, we propose the minimization of a non-convex functional for the solution of the CS problem. The considered functional incorporates information on the self-similarity of the image by measuring the rank of some appropriately constructed matrices of fairly small dimensions. However, since the rank minimization is a NP hard problem, we consider, as a surrogate function for the rank, a non-convex, but smooth function. We provide a theoretical analysis of the proposed functional and develop an iterative algorithm to compute one of its stationary points. We prove the convergence of such algorithm and show, with some selected numerical experiments, that the proposed approach achieves good performances, even when compared with the state of the art.
      PubDate: 2018-08-09
      DOI: 10.1007/s10444-018-9627-3
       
  • A deterministic sparse FFT for functions with structured Fourier sparsity
    • Authors: Sina Bittens; Ruochuan Zhang; Mark A. Iwen
      Abstract: In this paper, a deterministic sparse Fourier transform algorithm is presented which breaks the quadratic-in-sparsity runtime bottleneck for a large class of periodic functions exhibiting structured frequency support. These functions include, e.g., the often considered set of block frequency sparse functions of the form $$f(x) = \sum\limits^{n}_{j = 1} \sum\limits^{B-1}_{k = 0} c_{\omega_{j} + k} e^{i(\omega_{j} + k)x},~~\{ \omega_{1}, \dots, \omega_{n} \} \subset \left( -\left\lceil \frac{N}{2}\right\rceil, \left\lfloor \frac{N}{2}\right\rfloor\right]\cap\mathbb{Z}$$ as a simple subclass. Theoretical error bounds in combination with numerical experiments demonstrate that the newly proposed algorithms are both fast and robust to noise. In particular, they outperform standard sparse Fourier transforms in the rapid recovery of block frequency sparse functions of the type above.
      PubDate: 2018-08-09
      DOI: 10.1007/s10444-018-9626-4
       
  • Fast iterative solvers for an optimal transport problem
    • Authors: Roland Herzog; John W. Pearson; Martin Stoll
      Abstract: Optimal transport problems pose many challenges when considering their numerical treatment. We investigate the solution of a PDE-constrained optimisation problem subject to a particular transport equation arising from the modelling of image metamorphosis. We present the nonlinear optimisation problem, and discuss the discretisation and treatment of the nonlinearity via a Gauss–Newton scheme. We then derive preconditioners that can be used to solve the linear systems at the heart of the (Gauss–)Newton method.
      PubDate: 2018-08-07
      DOI: 10.1007/s10444-018-9625-5
       
  • Nonlocal operators with local boundary conditions in higher dimensions
    • Authors: Burak Aksoylu; Fatih Celiker; Orsan Kilicer
      Abstract: We present novel nonlocal governing operators in 2D/3D for wave propagation and diffusion. The operators are inspired by peridynamics. They agree with the original peridynamics operator in the bulk of the domain and simultaneously enforce local boundary conditions (BC). The main ingredients are periodic, antiperiodic, and mixed extensions of separable kernel functions together with even and odd parts of bivariate functions on rectangular/box domains. The operators are bounded and self-adjoint. We present all possible 36 different types of BC in 2D which include pure and mixed combinations of Neumann, Dirichlet, periodic, and antiperiodic BC. Our construction is systematic and easy to follow. We provide numerical experiments that verify our theoretical findings. We also compare the solutions of the classical wave and heat equations to their nonlocal counterparts.
      PubDate: 2018-08-02
      DOI: 10.1007/s10444-018-9624-6
       
 
 
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