移位和缩放吉尼布雷矩阵的 GMRES、伪谱和 Crouzeix 猜想

IF 2.2 2区 数学 Q1 MATHEMATICS, APPLIED
Tyler Chen, Anne Greenbaum, Thomas Trogdon
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引用次数: 0

摘要

我们研究了应用于线性方程组的 GMRES 算法,该方程组涉及一个经过缩放和移位的 N × N N 次矩阵,该矩阵的条目是独立的复高斯。当这个线性方程组的右边独立于这个随机矩阵时,GMRES残余误差的 N → ∞ Nto \infty 行为就可以精确地确定。为了处理右手侧依赖于随机矩阵的情况,我们研究了吉尼布雷矩阵的伪谱和数值范围,并证明了克鲁齐猜想的限制版本。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
GMRES, pseudospectra, and Crouzeix’s conjecture for shifted and scaled Ginibre matrices

We study the GMRES algorithm applied to linear systems of equations involving a scaled and shifted N × N N\times N matrix whose entries are independent complex Gaussians. When the right-hand side of this linear system is independent of this random matrix, the N N\to \infty behavior of the GMRES residual error can be determined exactly. To handle cases where the right hand side depends on the random matrix, we study the pseudospectra and numerical range of Ginibre matrices and prove a restricted version of Crouzeix’s conjecture.

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来源期刊
Mathematics of Computation
Mathematics of Computation 数学-应用数学
CiteScore
3.90
自引率
5.00%
发文量
55
审稿时长
7.0 months
期刊介绍: All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles of the highest quality in computational mathematics. Areas covered include numerical analysis, computational discrete mathematics, including number theory, algebra and combinatorics, and related fields such as stochastic numerical methods. Articles must be of significant computational interest and contain original and substantial mathematical analysis or development of computational methodology.
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