A New Choice of the Preconditioner of PHSS Method for Saddle Point Problems

SUN Jia, WANG Shi-heng, WANG Ke

doi:10.13371/j.cnki.chin.q.j.m.2015.04.008

Chinese Quarterly Journal of Mathematics >

2015 , Vol. 30 >Issue 4: 555 - 561

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2015.04.008

A New Choice of the Preconditioner of PHSS Method for Saddle Point Problems

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1. Department of Mathematics, Shanghai University2. Department of Automotive Engineering, Nanyang Vocational College of Agriculture

Biographies:WANGShi-heng(1965-), male, native of Nanyang, Henan, an associate professor of Nanyang Vocational College of Agriculture, M.S.D., engages in advanced algebra; WANG Ke(corresponding author)(1978-), male, native of Nanyang, Henan, a lecturer of Shanghai University, Ph.D., engages in numerical linear algebra and scientific computing.

Received date: 2014-01-22

Online published: 2020-11-19

Supported by

Supported by the National Natural Science Foundation of China(11301330)； Supported by the Shanghai College Teachers Visiting Abroad for Advanced Study Program（B.60-A101-12-010）； Supported by the First-class Discipline of Universities in Shanghai；

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Abstract

Bai, Golub and Pan presented a preconditioned Hermitian and skew-Hermitian splitting（PHSS） method [Numerische Mathematik, 2004, 32: 1-32] for non-Hermitian positive semidefinite linear systems. We improve the method to solve saddle point systems whose（1,1） block is a symmetric positive definite M-matrix with a new choice of the preconditioner and compare it with other preconditioners. The results show that the new preconditioner outperforms the previous ones.

Key words： saddle point problem; PHSS method; preconditioner

Cite this article

SUN Jia, WANG Shi-heng, WANG Ke . A New Choice of the Preconditioner of PHSS Method for Saddle Point Problems[J]. Chinese Quarterly Journal of Mathematics, 2015 , 30(4) : 555 -561 . DOI: 10.13371/j.cnki.chin.q.j.m.2015.04.008

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