近似结构伪谱
Approximated structured pseudospectra
AI总结：
本文提出一种基于选择合适秩一或投影秩一扰动计算矩阵伪谱和结构伪谱的新方法，通过分析特征值敏感性，提升计算效率和洞察力。
摘要：
伪谱和结构伪谱是分析矩阵的重要工具，但计算成本高。本文提出一种新方法，通过计算多个合适选择的秩一或投影秩一扰动的谱来近似伪谱和结构伪谱。该方法受Wilkinson对特征值敏感性的分析启发。数值示例显示，该方法比随机或结构随机秩一扰动在计算成本较低的情况下提供更深入的伪谱和结构伪谱洞察。后者目前常用于结构伪谱确定。
英文摘要：
Pseudospectra and structured pseudospectra are important tools for the analysis of matrices. Their computation, however, can be very demanding for all but small matrices. A new approach to compute approximations of pseudospectra and structured pseudospectra, based on determining the spectra of many suitably chosen rank-one or projected rank-one perturbations of the given matrix is proposed. The choice of rank-one or projected rank-one perturbations is inspired by Wilkinson's analysis of eigenvalue sensitivity. Numerical examples illustrate that the proposed approach gives much better insight into the pseudospectra and structured pseudospectra than random or structured random rank-one perturbations with lower computational burden. The latter approach is presently commonly used for the determination of structured pseudospectra.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
