Work

Structure of the preconditioned system in various preconditioned conjugate gradient squared algorithms

Year: 2019

Type: article

Abstract: An improved preconditioned conjugate gradient squared (PCGS) algorithm has recently been proposed, and it performs much better than the conventional PCGS algorithm. In this paper, the improved PCGS algorithm is verified as a coordinative to the left-preconditioned system, and it has the advantages of both the conventional and the left-PCGS; this is done by comparing, analyzing, and executing numerical examinations of various PCGS algorithms, including another improved one. We show that the direction of the preconditioned system for the CGS method is determined by the operations of αk and βk in the PCGS algorithm. By comparing the logical structures of these algorithms, we show that the direction of the preconditioned system can be switched by the construction and setting of the initial shadow residual vector.

Source: Results in Applied Mathematics

DOI: 10.1016/j.rinam.2019.100008

Authors: Shoji Itoh, Masaaki Sugihara

Institutions: Osaka Electro-Communication University, Aoyama Gakuin University

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $500

Funder: Japan Society for the Promotion of Science