2017/04/05 by Silvia Noschese, Noschese, Silvia, Lothar Reichel +1
Computer Science · Physics and Astronomy · #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Scientific Research and Discoveries
paper · pdf · doi:10.48550/arxiv.1704.01449
openalex publication_date 2017/04/05 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
In many applications it is important to understand the sensitivity of\neigenvalues of a matrix polynomial to perturbations of the polynomial. The\nsensitivity commonly is described by condition numbers or pseudospectra.\nHowever, the computation of pseudospectra of matrix polynomials is very\ndemanding computationally. This paper describes a new approach to computing\napproximations of pseudospectra of matrix polynomials by using rank-one or\nprojected rank-one perturbations. These perturbations are inspired by\nWilkinson's analysis of eigenvalue sensitivity. This approach allows the\napproximation of both structured and unstructured pseudospectra. Computed\nexamples show the method to perform much better than a method based on random\nrank-one perturbations both for the approximation of structured and\nunstructured (i.e., standard) polynomial pseudospectra.\n