Numerical Algorithms最新文献_第6页

Computation of polynomial and rational approximations in complex domains by the $$tau $$ -method 用 $$tau$ 方法计算复域中的多项式和有理近似值

IF 2.1 3区数学

Numerical Algorithms Pub Date : 2024-07-25 DOI: 10.1007/s11075-024-01897-7

Irina Georgieva, Clemens Hofreither

{"title":"Computation of polynomial and rational approximations in complex domains by the $$tau $$ -method","authors":"Irina Georgieva, Clemens Hofreither","doi":"10.1007/s11075-024-01897-7","DOIUrl":"https://doi.org/10.1007/s11075-024-01897-7","url":null,"abstract":"We investigate numerical methods for computation of polynomial and rational approximations of functions in complex domains based on Faber polynomials and the Lanczos (tau )-method. Our interest is motivated by applications in fractional partial differential equations. We give an overview of previous results related to the basis of Faber polynomials associated with a complex domain, Faber expansion, and the Lanczos (tau )-method. We also collect numerical algorithms for the computational realization of these concepts. Our main new contribution is a (tau )-method for rational approximation in complex domains which uses Faber polynomials in the perturbation term. We realize it via a novel hybrid symbolic-numeric algorithm which can be applied to arbitrary functions satisfying a suitable differential equation. We present some numerical examples, where we use sectors lying in the complex plane as our domains of interest. We compare results for the various polynomial and rational approximation techniques outlined above; in particular, we observe exponential convergence with respect to the rational degree for our proposed method.","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Unified convergence analysis of a class of iterative methods 一类迭代法的统一收敛分析

IF 2.1 3区数学

Numerical Algorithms Pub Date : 2024-07-24 DOI: 10.1007/s11075-024-01893-x

Muniyasamy M, Santhosh George, Chandhini G

引用次数: 0

On solving a revised model of the nonnegative matrix factorization problem by the modified adaptive versions of the Dai–Liao method 关于用戴廖法的修正自适应版本求解非负矩阵因式分解问题的修正模型

IF 2.1 3区数学

Numerical Algorithms Pub Date : 2024-07-24 DOI: 10.1007/s11075-024-01886-w

Saman Babaie-Kafaki, Fatemeh Dargahi, Zohre Aminifard

{"title":"On solving a revised model of the nonnegative matrix factorization problem by the modified adaptive versions of the Dai–Liao method","authors":"Saman Babaie-Kafaki, Fatemeh Dargahi, Zohre Aminifard","doi":"10.1007/s11075-024-01886-w","DOIUrl":"https://doi.org/10.1007/s11075-024-01886-w","url":null,"abstract":"We suggest a revised form of a classic measure function to be employed in the optimization model of the nonnegative matrix factorization problem. More exactly, using sparse matrix approximations, the revision term is embedded to the model for penalizing the ill-conditioning in the computational trajectory to obtain the factorization elements. Then, as an extension of the Euclidean norm, we employ the ellipsoid norm to gain adaptive formulas for the Dai–Liao parameter in a least-squares framework. In essence, the parametric choices here are obtained by pushing the Dai–Liao direction to the direction of a well-functioning three-term conjugate gradient algorithm. In our scheme, the well-known BFGS and DFP quasi–Newton updating formulas are used to characterize the positive definite matrix factor of the ellipsoid norm. To see at what level our model revisions as well as our algorithmic modifications are effective, we seek some numerical evidence by conducting classic computational tests and assessing the outputs as well. As reported, the results weigh enough value on our analytical efforts.","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Three families of $$C^1$$ - $$P_{2m+1}$$ Bell finite elements on triangular meshes 三角形网格上的三个 $$C^1$$ - $$P_{2m+1}$ Bell 有限元族

IF 2.1 3区数学

Numerical Algorithms Pub Date : 2024-07-24 DOI: 10.1007/s11075-024-01894-w

Xuejun Xu, Shangyou Zhang

{"title":"Three families of $$C^1$$ - $$P_{2m+1}$$ Bell finite elements on triangular meshes","authors":"Xuejun Xu, Shangyou Zhang","doi":"10.1007/s11075-024-01894-w","DOIUrl":"https://doi.org/10.1007/s11075-024-01894-w","url":null,"abstract":"The (C^1)-(P_5) Bell finite element removes the three degrees of freedom of the edge normal derivatives of the (C^1)-(P_5) Argyris finite element. We call a (C^1)-(P_k) finite element a Bell finite element if it has no edge-degree of freedom and it contains the (P_{k-1}) space locally. We construct three families of odd-degree (C^1)-(P_{2m+1}) Bell finite elements on triangular meshes. Comparing to the (C^1)-(P_{2m}) Argyris finite element, the (C^1)-(P_{2m+1}) Bell finite elements produce same-order solutions with much less unknowns. For example, the second (C^1)-(P_7) Bell element (from the second family) and the (C^1)-(P_6) Argyris element have numbers of local degrees of freedom of 31 and 28 respectively, but oppositely their numbers of global degrees of freedom are 12V and 19V asymptotically, respectively, where V is the number of vertices in a triangular mesh. A numerical example says the new element has about 3/4 number of unknowns, but is about 5 times more accurate. Numerical computations with all three families of elements are performed.","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Noise propagation in linear stationary iterations 线性静态迭代中的噪声传播

IF 2.1 3区数学

Numerical Algorithms Pub Date : 2024-07-23 DOI: 10.1007/s11075-024-01890-0

Tommy Elfving

引用次数: 0

TRIPs-Py: Techniques for regularization of inverse problems in python TRIPs-Py：Python 中的逆问题正则化技术

IF 2.1 3区数学

Numerical Algorithms Pub Date : 2024-07-22 DOI: 10.1007/s11075-024-01878-w

Mirjeta Pasha, Silvia Gazzola, Connor Sanderford, Ugochukwu O. Ugwu

{"title":"TRIPs-Py: Techniques for regularization of inverse problems in python","authors":"Mirjeta Pasha, Silvia Gazzola, Connor Sanderford, Ugochukwu O. Ugwu","doi":"10.1007/s11075-024-01878-w","DOIUrl":"https://doi.org/10.1007/s11075-024-01878-w","url":null,"abstract":"In this paper we describe TRIPs-Py, a new Python package of linear discrete inverse problems solvers and test problems. The goal of the package is two-fold: 1) to provide tools for solving small and large-scale inverse problems, and 2) to introduce test problems arising from a wide range of applications. The solvers available in TRIPs-Py include direct regularization methods (such as truncated singular value decomposition and Tikhonov) and iterative regularization techniques (such as Krylov subspace methods and recent solvers for (ell _p)-(ell _q) formulations, which enforce sparse or edge-preserving solutions and handle different noise types). All our solvers have built-in strategies to define the regularization parameter(s). Some of the test problems in TRIPs-Py arise from simulated image deblurring and computerized tomography, while other test problems model real problems in dynamic computerized tomography. Numerical examples are included to illustrate the usage as well as the performance of the described methods on the provided test problems. To the best of our knowledge, TRIPs-Py is the first Python software package of this kind, which may serve both research and didactical purposes.","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141737291","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Generalized analysis of methods for solving systems of nonlinear equations with point and interval coefficients 点系数和区间系数非线性方程组求解方法的广义分析

IF 2.1 3区数学

Numerical Algorithms Pub Date : 2024-07-20 DOI: 10.1007/s11075-024-01891-z

Alimzhan Ibragimov

{"title":"Generalized analysis of methods for solving systems of nonlinear equations with point and interval coefficients","authors":"Alimzhan Ibragimov","doi":"10.1007/s11075-024-01891-z","DOIUrl":"https://doi.org/10.1007/s11075-024-01891-z","url":null,"abstract":"In this article we consider problems of interval estimation of a set of solutions to point and interval (partially interval) systems of nonlinear equations. Most developed interval methods are intended only for estimating solutions of point nonlinear systems in some given interval box. And methods for estimating solution sets of nonlinear interval systems are not yet very developed, since the solution sets of such systems geometrically represent a rather complex structure. Here we conducted a general analysis on existing classical interval methods to test their applicability for interval systems. In this case, we chose the methods of Newton and Krawczyk. The results of the analysis show that these and similar other iterative methods are generally not applicable for interval systems due to the limited admissible area. Based on the results of the analysis, a new combined vertex method for outer estimation of solution sets of interval nonlinear systems is proposed, which includes these classical interval methods. Numerical experiments have shown that the proposed method is more efficient and gives more accurate estimates in feasible regions than the direct application of Newton, Krawczyk or Hansen-Sengupta interval methods for interval systems.","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141737292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Logarithmic norm minimization of quaternion matrix decomposition for color image sparse representation 用于彩色图像稀疏表示的四元数矩阵分解的对数规范最小化

IF 2.1 3区数学

Numerical Algorithms Pub Date : 2024-07-19 DOI: 10.1007/s11075-024-01887-9

Xiao-Min Cai, Yi-Fen Ke, Chang-Feng Ma, Ya-Jun Xie, Ri-Wei Liao

引用次数: 0

A treecode algorithm for the Poisson equation in a general domain with unstructured grids 非结构网格一般域中泊松方程的树形编码算法

IF 2.1 3区数学

Numerical Algorithms Pub Date : 2024-07-18 DOI: 10.1007/s11075-024-01888-8

Zixuan Cui, Lei Yang, Jing Wu, Guanghui Hu

{"title":"A treecode algorithm for the Poisson equation in a general domain with unstructured grids","authors":"Zixuan Cui, Lei Yang, Jing Wu, Guanghui Hu","doi":"10.1007/s11075-024-01888-8","DOIUrl":"https://doi.org/10.1007/s11075-024-01888-8","url":null,"abstract":"Since the seminal work in 1986, the treecode algorithm has been widely used in a variety of science and engineering problems, such as the electrostatic and magnetostatic fields calculations. With the continuous advancements of science exploration and engineering applications, efficient numerical simulations for problems defined on complex domains have become increasingly necessary. In this paper, based on a hierarchy geometry tree, an efficient implementation of the treecode algorithm is described in detail for the numerical solution of a Poisson equation defined on a general domain. The features of our algorithm include: i) with the hierarchy geometry tree, the neighbor and non-neighbor patches for a given element can be generated efficiently, ii) no restriction on the geometry of the domain, which means that our algorithm can be applied for general problem, iii) the desired computational complexity ({varvec{mathcal {O}}}(varvec{N},varvec{log },{varvec{N}})) can be observed well, where (varvec{N}) denotes the number of degrees of freedom in the domain, and iv) very friendly to the parallel computing, i.e., an ideal speedup can be observed successfully from numerical results with OpenMP technique. It is believed that our solution potentially is a quality candidate for implementing the treecode algorithm for problems defined on general domains with unstructured grids.","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141737179","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An Euler–Maruyama method for Caputo–Hadamard fractional stochastic differential equations on exponential meshes and its fast approximation 指数网格上的卡普托-哈达玛德分数随机微分方程的欧拉-丸山方法及其快速近似值

IF 2.1 3区数学

Numerical Algorithms Pub Date : 2024-07-18 DOI: 10.1007/s11075-024-01889-7

Min Li, Shangjiang Guo, Peng Hu, Haiyan Song

{"title":"An Euler–Maruyama method for Caputo–Hadamard fractional stochastic differential equations on exponential meshes and its fast approximation","authors":"Min Li, Shangjiang Guo, Peng Hu, Haiyan Song","doi":"10.1007/s11075-024-01889-7","DOIUrl":"https://doi.org/10.1007/s11075-024-01889-7","url":null,"abstract":"This paper studies the numerical solutions of Caputo–Hadamard fractional stochastic differential equations. Firstly, we construct an Euler–Maruyama (EM) scheme for the equations, and the corresponding convergence rate is investigated. Secondly, we propose a fast EM scheme based on the sum-of-exponentials approximation to decrease the computational cost of the EM scheme. More concretely, the fast EM scheme reduces the computational cost from (O(N^2)) to (O(Nlog ^2 N)) and the storage from O(N) to (O(log ^2 N)) when the final time (Tapprox e), where N is the total number of time steps. Moreover, considering the statistical errors from Monte Carlo path approximations, multilevel Monte Carlo (MLMC) techniques are utilized to reduce computational complexity. In particular, for a prescribed accuracy (varepsilon >0), the EM scheme and the fast EM scheme, integrated with the MLMC technique, respectively reduce the standard EM scheme’s computational complexity from (O(varepsilon ^{-2-frac{2}{widetilde{alpha }}})) to (O(varepsilon ^{-frac{2}{widetilde{alpha }}})) and the fast EM scheme’s complexity to (O(varepsilon ^{-frac{1}{widetilde{alpha }}}left|log varepsilon right|^3)), where (0<widetilde{alpha }=alpha -frac{1}{2}<frac{1}{2}). Finally, numerical examples are included to verify the theoretical results and demonstrate the performance of our methods.","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141737293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0