This article is cited in 2 papers

General numerical methods

Computation of asymptotic spectral distributions for sequences of grid operators

S. V. Morozov^ab, S. Serra-Capizzano^cd, E. E. Tyrtyshnikov<sup>abef

a</sup> Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991 Russia
^b Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, 119333 Russia
^c University of Insubria, Como, 22100 Italy
^d Uppsala University, Uppsala, SE-751 05 Sweden
^e Siedlce University, Siedlce, 08-110 Poland
^f Moscow Center for Fundamental and Applied Mathematics, Moscow, 119234 Russia

Abstract: The asymptotic spectral properties of matrices of grid operators on polygonal domains in the plane are studied in the case of refining triangular grids. Methods available for analyzing spectral distributions are largely based on tool of the theory of generalized locally Toeplitz sequences (GLT theory). In this paper, we show that the matrices of grid operators on nonrectangular domains do not form GLT sequences. A method for calculating spectral distributions in such cases is proposed. Generalizations of GLT sequences are introduced, and preconditioner based on them are proposed.

Key words: Toeplitz matrices, locally Toeplitz sequences, GLT sequences, discretization of partial differential equations, eigenvalues, singular values, preconditioning.

UDC: 517.983.3+512.643.8+519.62

Received: 23.03.2020
Revised: 11.05.2020
Accepted: 07.07.2020

DOI: 10.31857/S0044466920110095

 English version: Computational Mathematics and Mathematical Physics, 2020, 60:11, 1761–1777

Bibliographic databases:

• 
• 
•