One of the most computationally expensive problems in numerical linear algebra is the computation of the ∈-pseudospectrum of matrices, that is, the locus of eigenvalues of all matrices of the form A + E, where ||E|| ≤ ∈. Several research efforts have been attempting to make the problem tractable by means of better algorithms and utilization of all possible computational resources. One common goal is to bring to users the power to extract pseudospectrum information from their applications, on the computational environments they generally use, at a cost that is sufficiently low to render these computations routine. To this end, we investigate a scheme based on i) iterative methods for computing pseudospectra via approximations of the resolvent norm, with ii) a computational platform based on a cluster of PCs and iii) a programming environment based on MATLAB enhanced with MPI functionality and show that it can achieve high performance for problems of significant size.
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机译：数值线性代数中最昂贵的问题之一是矩阵的∈-PseutoSpectrum的计算，即，形式A + e的所有矩阵的特征值的基因座，其中|| e || ≤∈。几项研究努力一直试图通过更好的算法和所有可能的计算资源利用算法来实现问题。一个共同目标是为用户提供从他们的应用程序中提取伪谱信息的权力，在他们通常使用的计算环境中，以足够低的成本来呈现这些计算例程。为此，我们研究了基于I）通过基于PCS和III集群的分辨率规范的近似计算伪谱来计算伪谱的迭代方法，其中基于PCS和III的群集基于MATLAB的编程环境增强了MPI功能表明它可以实现高性能的尺寸问题。
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