最接近旋转矩阵问题的求解方法:比较综述

IF 1.8 3区数学 Q1 MATHEMATICS

Numerical Linear Algebra with Applications Pub Date : 2023-01-21 DOI:10.1002/nla.2492

Soheil Sarabandi, Federico Thomas

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引用次数: 1

摘要

目前，奇异值分解(SVD)是求解最近旋转矩阵问题的标准方法。然而，许多其他的方法是可用的在三维情况下的文献。本文综述了最具代表性的几种方法，提出了几种替代方法，并进行了比较分析，以阐明它们的相对计算成本和误差性能。这一分析得出的结论是，一些代数闭形方法与奇异值分解一样鲁棒，但速度更快，更准确。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Solution methods to the nearest rotation matrix problem in ℝ3 : A comparative survey

Nowadays, the singular value decomposition (SVD) is the standard method of choice for solving the nearest rotation matrix problem. Nevertheless, many other methods are available in the literature for the 3D case. This article reviews the most representative ones, proposes alternative ones, and presents a comparative analysis to elucidate their relative computational costs and error performances. This analysis leads to the conclusion that some algebraic closed‐form methods are as robust as the SVD, but significantly faster and more accurate.

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来源期刊

Numerical Linear Algebra with Applications 数学-数学

CiteScore

3.40

自引率

2.30%

发文量

审稿时长

12 months

期刊介绍： Manuscripts submitted to Numerical Linear Algebra with Applications should include large-scale broad-interest applications in which challenging computational results are integral to the approach investigated and analysed. Manuscripts that, in the Editor’s view, do not satisfy these conditions will not be accepted for review. Numerical Linear Algebra with Applications receives submissions in areas that address developing, analysing and applying linear algebra algorithms for solving problems arising in multilinear (tensor) algebra, in statistics, such as Markov Chains, as well as in deterministic and stochastic modelling of large-scale networks, algorithm development, performance analysis or related computational aspects. Topics covered include: Standard and Generalized Conjugate Gradients, Multigrid and Other Iterative Methods; Preconditioning Methods; Direct Solution Methods; Numerical Methods for Eigenproblems; Newton-like Methods for Nonlinear Equations; Parallel and Vectorizable Algorithms in Numerical Linear Algebra; Application of Methods of Numerical Linear Algebra in Science, Engineering and Economics.