arXiv - CS - Numerical Analysis最新文献_第9页

The Akhiezer iteration Akhiezer迭代

arXiv - CS - Numerical Analysis Pub Date : 2023-12-04 DOI: arxiv-2312.02384

Cade Ballew, Thomas Trogdon

引用次数: 0

Mathematical Supplement for the $texttt{gsplat}$ Library $texttt{gsplat}$图书馆的数学补充

arXiv - CS - Numerical Analysis Pub Date : 2023-12-04 DOI: arxiv-2312.02121

Vickie Ye, Angjoo Kanazawa

引用次数: 0

Lecture Notes on Computerized Tomography 计算机断层扫描课堂讲稿

arXiv - CS - Numerical Analysis Pub Date : 2023-12-04 DOI: arxiv-2312.02393

Matthias Beckmann

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Numerical approximation of Dynkin games with asymmetric information 具有非对称信息的Dynkin博弈的数值逼近

arXiv - CS - Numerical Analysis Pub Date : 2023-12-04 DOI: arxiv-2312.01847

Ľubomír Baňas, Giorgio Ferrari, Tsiry Avisoa Randrianasolo

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Using Bayesian Optimization to Design Time Step Size Controllers with Application to Modified Patankar--Runge--Kutta Methods 基于改进Patankar—Runge—Kutta方法的贝叶斯优化设计时间步长控制器

arXiv - CS - Numerical Analysis Pub Date : 2023-12-04 DOI: arxiv-2312.01796

Thomas Izgin, Hendrik Ranocha

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Fast Fourier Transform periodic interpolation method for superposition sums in a periodic unit cell 周期单元格中叠加和的快速傅里叶变换周期插值方法

arXiv - CS - Numerical Analysis Pub Date : 2023-12-04 DOI: arxiv-2312.02376

Fangzhou Ai, Vitaliy Lomakin

{"title":"Fast Fourier Transform periodic interpolation method for superposition sums in a periodic unit cell","authors":"Fangzhou Ai, Vitaliy Lomakin","doi":"arxiv-2312.02376","DOIUrl":"https://doi.org/arxiv-2312.02376","url":null,"abstract":"We propose a Fast Fourier Transform based Periodic Interpolation Method\u0000(FFT-PIM), a flexible and computationally efficient approach for computing the\u0000scalar potential given by a superposition sum in a unit cell of an infinitely\u0000periodic array. Under the same umbrella, FFT-PIM allows computing the potential\u0000for 1D, 2D, and 3D periodicities for dynamic and static problems, including\u0000problems with and without a periodic phase shift. The computational complexity\u0000of the FFT-PIM is of $O(N log N)$ for $N$ spatially coinciding sources and\u0000observer points. The FFT-PIM uses rapidly converging series representations of\u0000the Green's function serving as a kernel in the superposition sum. Based on\u0000these representations, the FFT-PIM splits the potential into its near-zone\u0000component, which includes a small number of images surrounding the unit cell of\u0000interest, and far-zone component, which includes the rest of an infinite number\u0000of images. The far-zone component is evaluated by projecting the non-uniform\u0000sources onto a sparse uniform grid, performing superposition sums on this\u0000sparse grid, and interpolating the potential from the uniform grid to the\u0000non-uniform observation points. The near-zone component is evaluated using an\u0000FFT-based method, which is adapted to efficiently handle non-uniform\u0000source-observer distributions within the periodic unit cell. The FFT-PIM can be\u0000used for a broad range of applications, such as periodic problems involving\u0000integral equations in computational electromagnetic and acoustic, micromagnetic\u0000solvers, and density functional theory solvers.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":" 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A $W$-weighted generalization of ${1,2,3,1^{k}}$-inverse for rectangular matrices 矩形矩阵${1,2,3,1^{k}}$-逆的$W$加权概化

arXiv - CS - Numerical Analysis Pub Date : 2023-12-03 DOI: arxiv-2312.01370

Geeta Chowdhry, Falguni Roy

{"title":"A $W$-weighted generalization of ${1,2,3,1^{k}}$-inverse for rectangular matrices","authors":"Geeta Chowdhry, Falguni Roy","doi":"arxiv-2312.01370","DOIUrl":"https://doi.org/arxiv-2312.01370","url":null,"abstract":"This paper presents a novel extension of the ${1,2,3,1^{k}}$-inverse\u0000concept to complex rectangular matrices, denoted as a $W$-weighted\u0000${1,2,3,1^{k}}$-inverse (or ${1',2',3',{1^{k}}'}$-inverse), where the\u0000weight $W in mathbb{C}^{n times m}$. The study begins by introducing a\u0000weighted ${1,2,3}$-inverse (or ${1',2',3'}$-inverse) along with its\u0000representations and characterizations. The paper establishes criteria for the\u0000existence of ${1',2',3'}$-inverses and extends the criteria to\u0000${1'}$-inverses. It is further demonstrated that $Ain mathbb{C}^{m times\u0000n}$ admits a ${1',2',3',{1^{k}}'}$-inverse if and only if $r(WAW)=r(A)$,\u0000where $r(cdot)$ is the rank of a matrix. The work additionally establishes\u0000various representations for the set $A{ 1',2',3',{1^{k}}'}$, including\u0000canonical representations derived through singular value and core-nilpotent\u0000decompositions. This, in turn, yields distinctive canonical representations for\u0000the set $A{ 1,2,3,{1^{k}}}$. ${ 1',2',3',{1^{k}}'}$-inverse is shown to be\u0000unique if and only if it has index $0$ or $1$, reducing it to the weighted core\u0000inverse. Moreover, the paper investigates properties and characterizations of\u0000${1',2',3',{1^{k}}'}$-inverses, which then results in new insights into the\u0000characterizations of the set $A{ 1,2,3,{1^{k}}}$.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":" 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Driven transparent quantum graphs 驱动透明量子图

arXiv - CS - Numerical Analysis Pub Date : 2023-12-03 DOI: arxiv-2312.01448

J. R. Yusupov, M. Ehrhardt, Kh. Sh. Matyokubov, D. U. Matrasulov

引用次数: 0

A New Upper Bound For the Growth Factor in Gaussian Elimination with Complete Pivoting 完全旋转高斯消去中生长因子的一个新的上界

arXiv - CS - Numerical Analysis Pub Date : 2023-12-02 DOI: arxiv-2312.00994

Ankit Bisain, Alan Edelman, John Urschel

引用次数: 0

The time dimensional reduction method to determine the initial conditions for nonlinear and nonlocal hyperbolic equations 确定非线性非局部双曲型方程初始条件的时间降维方法

arXiv - CS - Numerical Analysis Pub Date : 2023-12-02 DOI: arxiv-2312.01179

Trong D. Dang, Loc H. Nguyen, Huong T. T. Vu

引用次数: 0