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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2023 Volume 63, Number 5, Page 715 (Mi zvmmf11546)

General numerical methods

A generalized simplified Hermitian and skew-Hermitian splitting preconditioner for double saddle point problems

L. Menga, Y. W. Heab, J. Lia

a College of Mathematics and Statistics, Northwest Normal University 730070 Lanzhou, P. R. China
b Institute for Advanced Study in History of Science, Northwest University 710127 Xi’an, P. R. China

Abstract: In this work, we mainly propose a generalized simplified Hermitian and skew-Hermitian splitting (GSHSS) preconditioner for solving double saddle point problems and the eigenvalue distribution of the GSHSS preconditioner is analyzed in detail. In addition, we also study the eigenvector distribution and the degree of the minimal polynomial of the preconditioned matrix. Finally, numerical experiments show the effectiveness of the proposed preconditioner.

Key words: double saddle point problems, preconditioning, spectral properties, Krylov subspace method.

UDC: 519.612

Received: 25.11.2021
Revised: 05.12.2022
Accepted: 02.02.2023

Language: English

DOI: 10.31857/S0044466923050149


 English version:
Computational Mathematics and Mathematical Physics, 2023, 63:5, 704–718

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© Steklov Math. Inst. of RAS, 2026