BIT Numerical Mathematics最新文献_第3页

Convergence and superconvergence of a fractional collocation method for weakly singular Volterra integro-differential equations 弱奇异 Volterra 积分微分方程的分数配位法的收敛性和超收敛性

IF 1.5 3区数学

BIT Numerical Mathematics Pub Date : 2024-02-12 DOI: 10.1007/s10543-024-01011-2

引用次数: 0

A convolution quadrature using derivatives and its application 使用导数的卷积正交及其应用

IF 1.5 3区数学

BIT Numerical Mathematics Pub Date : 2024-02-09 DOI: 10.1007/s10543-024-01009-w

Hao Ren, Junjie Ma, Huilan Liu

引用次数: 0

A posteriori error estimates for a dual finite element method for singularly perturbed reaction–diffusion problems 奇异扰动反应扩散问题二元有限元法的后验误差估计

IF 1.5 3区数学

BIT Numerical Mathematics Pub Date : 2024-02-05 DOI: 10.1007/s10543-024-01008-x

JaEun Ku, Martin Stynes

引用次数: 0

Improved uniform error bounds on parareal exponential algorithm for highly oscillatory systems 高振荡系统准指数算法的改进均匀误差边界

IF 1.5 3区数学

BIT Numerical Mathematics Pub Date : 2024-01-31 DOI: 10.1007/s10543-023-01005-6

Bin Wang, Yaolin Jiang

{"title":"Improved uniform error bounds on parareal exponential algorithm for highly oscillatory systems","authors":"Bin Wang, Yaolin Jiang","doi":"10.1007/s10543-023-01005-6","DOIUrl":"https://doi.org/10.1007/s10543-023-01005-6","url":null,"abstract":"For the well known parareal algorithm, we formulate and analyse a novel class of parareal exponential schemes with improved uniform accuracy for highly oscillatory system (ddot{q}+frac{1}{varepsilon ^2}M q =frac{1}{varepsilon ^{mu }}f(q)) with (mu =0) or 1. The solution of this considered system propagates waves with wavelength at (mathcal {O} (varepsilon )) in time and the value of (mu ) corresponds to the strength of nonlinearity. This brings significantly numerical burden in scientific computation for highly oscillatory systems with (0<varepsilon ll 1). The new proposed algorithm is formulated by using some reformulation approaches to the problem, Fourier pseudo-spectral methods, and parareal exponential integrators. The fast Fourier transform is incorporated in the implementation. We rigorously study the convergence, showing that for nonlinear systems, the algorithm has improved uniform accuracy (mathcal {O}big ( varepsilon ^{(2k+3)(1-mu )}Delta t^{2k+2}+varepsilon ^{5(1-mu )}delta t^4big )) in the position and (mathcal {O}big ( varepsilon ^{(2k+3)(1-mu )-1}Delta t^{2k+2}+varepsilon ^{4-5mu }delta t^4big )) in the momenta, where k is the number of parareal iterations, and (Delta t) and (delta t) are two time stepsizes used in the algorithm. The energy conservation is also discussed and the algorithm is shown to have an improved energy conservation. Numerical experiments are provided and the numerical results demonstrate the improved uniform accuracy and improved energy conservation of the obtained integrator through four Hamiltonian differential equations including nonlinear wave equations.","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":"8 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139648530","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

On the stability radius for linear time-delay systems 论线性时延系统的稳定半径

IF 1.5 3区数学

BIT Numerical Mathematics Pub Date : 2024-01-30 DOI: 10.1007/s10543-023-01006-5

引用次数: 0

Incremental algorithms for truncated higher-order singular value decompositions 截断高阶奇异值分解的增量算法

IF 1.5 3区数学

BIT Numerical Mathematics Pub Date : 2024-01-08 DOI: 10.1007/s10543-023-01004-7

Chao Zeng, Michael K. Ng, Tai-Xiang Jiang

引用次数: 0

A regularization–correction approach for adapting subdivision schemes to the presence of discontinuities 使细分方案适应不连续性的正则化修正方法

IF 1.5 3区数学

BIT Numerical Mathematics Pub Date : 2024-01-04 DOI: 10.1007/s10543-023-01003-8

Sergio Amat, David Levin, Juan Ruiz-Álvarez, Dionisio F. Yáñez

{"title":"A regularization–correction approach for adapting subdivision schemes to the presence of discontinuities","authors":"Sergio Amat, David Levin, Juan Ruiz-Álvarez, Dionisio F. Yáñez","doi":"10.1007/s10543-023-01003-8","DOIUrl":"https://doi.org/10.1007/s10543-023-01003-8","url":null,"abstract":"Linear approximation methods suffer from Gibbs oscillations when approximating functions with jumps. Essentially non oscillatory subcell-resolution (ENO-SR) is a local technique avoiding oscillations and with a full order of accuracy, but a loss of regularity of the approximant appears. The goal of this paper is to introduce a new approach having both properties of full accuracy and regularity. In order to obtain it, we propose a three-stage algorithm: first, the data is smoothed by subtracting an appropriate non-smooth data sequence; then a chosen high order linear approximation operator is applied to the smoothed data and finally, an approximation with the proper jump or corner (jump in the first order derivative) discontinuity structure is reinstated by correcting the smooth approximation with the non-smooth element used in the first stage. This new procedure can be applied as subdivision scheme to design curves and surfaces both in point-value and in cell-average contexts. Using the proposed algorithm, we are able to construct approximations with high precision, with high piecewise regularity, and without smearing nor oscillations in the presence of discontinuities. These are desired properties in real applications as computer aided design or car design, among others.","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":"43 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139094502","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

Block diagonal Calderón preconditioning for scattering at multi-screens. 针对多屏幕散射的块对角卡尔德隆预处理。

IF 1.6 3区数学

BIT Numerical Mathematics Pub Date : 2024-01-01 Epub Date: 2024-09-03 DOI: 10.1007/s10543-024-01034-9

Kristof Cools, Carolina Urzúa-Torres

引用次数: 0

From low-rank retractions to dynamical low-rank approximation and back. 从低阶回缩到动态低阶近似，再回到低阶近似。

IF 1.6 3区数学

BIT Numerical Mathematics Pub Date : 2024-01-01 Epub Date: 2024-06-17 DOI: 10.1007/s10543-024-01028-7

Axel Séguin, Gianluca Ceruti, Daniel Kressner

{"title":"From low-rank retractions to dynamical low-rank approximation and back.","authors":"Axel Séguin, Gianluca Ceruti, Daniel Kressner","doi":"10.1007/s10543-024-01028-7","DOIUrl":"10.1007/s10543-024-01028-7","url":null,"abstract":"In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for other computational tasks on manifold as well, including interpolation tasks. In this work, we consider the application of retractions to the numerical integration of differential equations on fixed-rank matrix manifolds. This is closely related to dynamical low-rank approximation (DLRA) techniques. In fact, any retraction leads to a numerical integrator and, vice versa, certain DLRA techniques bear a direct relation with retractions. As an example for the latter, we introduce a new retraction, called KLS retraction, that is derived from the so-called unconventional integrator for DLRA. We also illustrate how retractions can be used to recover known DLRA techniques and to design new ones. In particular, this work introduces two novel numerical integration schemes that apply to differential equations on general manifolds: the accelerated forward Euler (AFE) method and the Projected Ralston-Hermite (PRH) method. Both methods build on retractions by using them as a tool for approximating curves on manifolds. The two methods are proven to have local truncation error of order three. Numerical experiments on classical DLRA examples highlight the advantages and shortcomings of these new methods.","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":"64 3","pages":"25"},"PeriodicalIF":1.6,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11182878/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141428320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Analysis of eigenvalue condition numbers for a class of randomized numerical methods for singular matrix pencils. 奇异矩阵铅笔的一类随机数值方法的特征值条件数分析。

IF 1.6 3区数学

BIT Numerical Mathematics Pub Date : 2024-01-01 Epub Date: 2024-07-15 DOI: 10.1007/s10543-024-01033-w

Daniel Kressner, Bor Plestenjak

{"title":"Analysis of eigenvalue condition numbers for a class of randomized numerical methods for singular matrix pencils.","authors":"Daniel Kressner, Bor Plestenjak","doi":"10.1007/s10543-024-01033-w","DOIUrl":"https://doi.org/10.1007/s10543-024-01033-w","url":null,"abstract":"The numerical solution of the generalized eigenvalue problem for a singular matrix pencil is challenging due to the discontinuity of its eigenvalues. Classically, such problems are addressed by first extracting the regular part through the staircase form and then applying a standard solver, such as the QZ algorithm, to that regular part. Recently, several novel approaches have been proposed to transform the singular pencil into a regular pencil by relatively simple randomized modifications. In this work, we analyze three such methods by Hochstenbach, Mehl, and Plestenjak that modify, project, or augment the pencil using random matrices. All three methods rely on the normal rank and do not alter the finite eigenvalues of the original pencil. We show that the eigenvalue condition numbers of the transformed pencils are unlikely to be much larger than the <math><mi>δ</mi></math> -weak eigenvalue condition numbers, introduced by Lotz and Noferini, of the original pencil. This not only indicates favorable numerical stability but also reconfirms that these condition numbers are a reliable criterion for detecting simple finite eigenvalues. We also provide evidence that, from a numerical stability perspective, the use of complex instead of real random matrices is preferable even for real singular matrix pencils and real eigenvalues. As a side result, we provide sharp left tail bounds for a product of two independent random variables distributed with the generalized beta distribution of the first kind or Kumaraswamy distribution.","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":"64 3","pages":"32"},"PeriodicalIF":1.6,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11249782/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141635867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0