Year: 2024
Type: preprint
Abstract: We propose a continuous approach to computing the pseudospectra of linear operators with compact or compact-plus-scalar resolvent, following a 'solve-then-discretize' strategy. Instead of taking a finite section approach or using a finite-dimensional matrix to approximate the operator of interest, the new method employs an operator analogue of the Lanczos process to work with operators and functions directly. The method is shown to be free of spectral pollution and spectral invisibility, fully adaptive, and nearly optimal in accuracy. The advantages of the method are demonstrated by extensive numerical examples and comparison with the traditional method.
Source: arXiv (Cornell University)
Authors: Deng, Kuan, Liu, Xiaolin, Xu, Kuan
Institution: University of Science and Technology of China
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4396787152