SIAM Journal on Numerical Analysis最新文献_第2页

The Lanczos Tau Framework for Time-Delay Systems: Padé Approximation and Collocation Revisited 时延系统的 Lanczos Tau 框架：帕代逼近与重新定位

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-11-13 DOI: 10.1137/24m164611x

Evert Provoost, Wim Michiels

引用次数: 0

Spherical Designs for Approximations on Spherical Caps 球形帽上的近似球形设计

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-11-11 DOI: 10.1137/23m1555417

Chao Li, Xiaojun Chen

{"title":"Spherical Designs for Approximations on Spherical Caps","authors":"Chao Li, Xiaojun Chen","doi":"10.1137/23m1555417","DOIUrl":"https://doi.org/10.1137/23m1555417","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 6, Page 2506-2528, December 2024. Abstract. A spherical [math]-design is a set of points on the unit sphere, which provides an equal weight quadrature rule integrating exactly all spherical polynomials of degree at most [math] and has a sharp error bound for approximations on the sphere. This paper introduces a set of points called a spherical cap [math]-subdesign on a spherical cap [math] with center [math] and radius [math] induced by the spherical [math]-design. We show that the spherical cap [math]-subdesign provides an equal weight quadrature rule integrating exactly all zonal polynomials of degree at most [math] and all functions expanded by orthonormal functions on the spherical cap which are defined by shifted Legendre polynomials of degree at most [math]. We apply the spherical cap [math]-subdesign and the orthonormal basis functions on the spherical cap to non-polynomial approximation of continuous functions on the spherical cap and present theoretical approximation error bounds. We also apply spherical cap [math]-subdesigns to sparse signal recovery on the upper hemisphere, which is a spherical cap with [math]. Our theoretical and numerical results show that spherical cap [math]-subdesigns can provide a good approximation on spherical caps.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"153 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142598300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 Operator Preconditioned Combined Field Integral Equation for Electromagnetic Scattering 电磁散射的算子预处理组合场积分方程

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-11-07 DOI: 10.1137/23m1581674

Van Chien Le, Kristof Cools

引用次数: 0

An Energy-Based Discontinuous Galerkin Method for the Nonlinear Schrödinger Equation with Wave Operator 带波算子的非线性薛定谔方程的基于能量的非连续伽勒金方法

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-11-04 DOI: 10.1137/23m1597496

Kui Ren, Lu Zhang, Yin Zhou

{"title":"An Energy-Based Discontinuous Galerkin Method for the Nonlinear Schrödinger Equation with Wave Operator","authors":"Kui Ren, Lu Zhang, Yin Zhou","doi":"10.1137/23m1597496","DOIUrl":"https://doi.org/10.1137/23m1597496","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 6, Page 2459-2483, December 2024. Abstract. This work develops an energy-based discontinuous Galerkin (EDG) method for the nonlinear Schrödinger equation with the wave operator. The focus of the study is on the energy-conserving or energy-dissipating behavior of the method with some simple mesh-independent numerical fluxes we designed. We establish error estimates in the energy norm that require careful selection of a weak formulation for the auxiliary equation involving the time derivative of the displacement variable. A critical part of the convergence analysis is to establish the [math] error bounds for the time derivative of the approximation error in the displacement variable by using the equation that determines its mean value. Using a special weak formulation, we show that one can create a linear system for the time evolution of the unknowns even when dealing with nonlinear properties in the original problem. Numerical experiments were performed to demonstrate the optimal convergence of the scheme in the [math] norm. These experiments involved specific choices of numerical fluxes combined with specific choices of approximation spaces.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"10 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142580294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 Equilibrated Flux A Posteriori Error Estimator for Defeaturing Problems 失效问题的平衡通量后验误差估算器

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-11-04 DOI: 10.1137/23m1627195

Annalisa Buffa, Ondine Chanon, Denise Grappein, Rafael Vázquez, Martin Vohralík

{"title":"An Equilibrated Flux A Posteriori Error Estimator for Defeaturing Problems","authors":"Annalisa Buffa, Ondine Chanon, Denise Grappein, Rafael Vázquez, Martin Vohralík","doi":"10.1137/23m1627195","DOIUrl":"https://doi.org/10.1137/23m1627195","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 6, Page 2439-2458, December 2024. Abstract. An a posteriori error estimator based on an equilibrated flux reconstruction is proposed for defeaturing problems in the context of finite element discretizations. Defeaturing consists in the simplification of a geometry by removing features that are considered not relevant for the approximation of the solution of a given PDE. In this work, the focus is on a Poisson equation with Neumann boundary conditions on the feature boundary. The estimator accounts both for the so-called defeaturing error and for the numerical error committed by approximating the solution on the defeatured domain. Unlike other estimators that were previously proposed for defeaturing problems, the use of the equilibrated flux reconstruction allows us to obtain a sharp bound for the numerical component of the error. Furthermore, it does not require the evaluation of the normal trace of the numerical flux on the feature boundary: this makes the estimator well suited for finite element discretizations, in which the normal trace of the numerical flux is typically discontinuous across elements. The reliability of the estimator is proven and verified on several numerical examples. Its capability to identify the most relevant features is also shown, in anticipation of a future application to an adaptive strategy.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"41 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142580295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

The A Posteriori Error Estimates of the FE Approximation of Defective Eigenvalues for Non-Self-Adjoint Eigenvalue Problems 非自相交特征值问题的缺陷特征值 FE 近似的后验误差估计值

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-11-04 DOI: 10.1137/23m162065x

Yidu Yang, Shixi Wang, Hai Bi

引用次数: 0

Erratum: Analysis and Numerical Approximation of Stationary Second-Order Mean Field Game Partial Differential Inclusions 勘误：静态二阶均值场博弈偏微分夹杂的分析与数值逼近

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-10-22 DOI: 10.1137/24m165123x

Yohance A. P. Osborne, Iain Smears

引用次数: 0

Achieving High Convergence Rates by Quasi-Monte Carlo and Importance Sampling for Unbounded Integrands 用准蒙特卡罗和重要性采样实现无界积分的高收敛率

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-10-21 DOI: 10.1137/23m1622489

Du Ouyang, Xiaoqun Wang, Zhijian He

{"title":"Achieving High Convergence Rates by Quasi-Monte Carlo and Importance Sampling for Unbounded Integrands","authors":"Du Ouyang, Xiaoqun Wang, Zhijian He","doi":"10.1137/23m1622489","DOIUrl":"https://doi.org/10.1137/23m1622489","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 5, Page 2393-2414, October 2024. Abstract. We consider the problem of estimating an expectation [math] by quasi-Monte Carlo (QMC) methods, where [math] is an unbounded smooth function and [math] is a standard normal random vector. While the classical Koksma–Hlawka inequality cannot be directly applied to unbounded functions, we establish a novel framework to study the convergence rates of QMC for unbounded smooth integrands. We propose a projection method to modify the unbounded integrands into bounded and smooth ones, which differs from the low variation extension strategy of avoiding the singularities along the boundary of the unit cube [math] in Owen [SIAM Rev., 48 (2006), pp. 487–503]. The total error is then bounded by the quadrature error of the transformed integrand and the projection error. We prove that if the function [math] and its mixed partial derivatives do not grow too fast as the Euclidean norm [math] tends to infinity, then projection-based QMC and randomized QMC (RQMC) methods achieve an error rate of [math] with a sample size [math] and an arbitrarily small [math]. However, the error rate turns out to be only [math] when the functions grow exponentially as [math] with [math]. Remarkably, we find that using importance sampling with [math]-distribution as the proposal can dramatically improve the root mean squared error of RQMC from [math] to [math].","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"125 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142486666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

How Sharp Are Error Bounds? –Lower Bounds on Quadrature Worst-Case Errors for Analytic Functions– 误差界限有多精确？-解析函数的正交最差误差下限--

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-10-18 DOI: 10.1137/24m1634163

Takashi Goda, Yoshihito Kazashi, Ken’ichiro Tanaka

{"title":"How Sharp Are Error Bounds? –Lower Bounds on Quadrature Worst-Case Errors for Analytic Functions–","authors":"Takashi Goda, Yoshihito Kazashi, Ken’ichiro Tanaka","doi":"10.1137/24m1634163","DOIUrl":"https://doi.org/10.1137/24m1634163","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 5, Page 2370-2392, October 2024. Abstract. Numerical integration over the real line for analytic functions is studied. Our main focus is on the sharpness of the error bounds. We first derive two general lower estimates for the worst-case integration error, and then apply these to establish lower bounds for various quadrature rules. These bounds turn out to either be novel or improve upon existing results, leading to lower bounds that closely match upper bounds for various formulas. Specifically, for the suitably truncated trapezoidal rule, we improve upon general lower bounds on the worst-case error obtained by Sugihara [Numer. Math., 75 (1997), pp. 379–395] and provide exceptionally sharp lower bounds apart from a polynomial factor, and in particular we show that the worst-case error for the trapezoidal rule by Sugihara is not improvable by more than a polynomial factor. Additionally, our research reveals a discrepancy between the error decay of the trapezoidal rule and Sugihara’s lower bound for general numerical integration rules, introducing a new open problem. Moreover, the Gauss–Hermite quadrature is proven suboptimal under the decay conditions on integrands we consider, a result not deducible from upper-bound arguments alone. Furthermore, to establish the near-optimality of the suitably scaled Gauss–Legendre and Clenshaw–Curtis quadratures, we generalize a recent result of Trefethen [SIAM Rev., 64 (2022), pp. 132–150] for the upper error bounds in terms of the decay conditions.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"62 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142449547","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Fractal Multiquadric Interpolation Functions 分形多四边形插值函数

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-10-18 DOI: 10.1137/23m1578917

D. Kumar, A. K. B. Chand, P. R. Massopust

引用次数: 0