Convergence analysis of projected SOR iteration method for a class of vertical linear complementarity problems

• Published in: Computational & applied mathematics Vol. 42; no. 4
• Main Authors: Cao, Yang, Yang, Geng-Chen, Shen, Qin-Qin
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01-06-2023; Springer Nature B.V
• Subjects: Applications of Mathematics; Applied physics; Computational mathematics; Computational Mathematics and Numerical Analysis; Convergence; Iterative methods; Mathematical analysis; Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematics; Mathematics and Statistics; Matrices (mathematics); Splitting; 65F50; Vertical linear complementarity problem; SOR iteration; 65F10; Matrix splitting; Projected method; Convergence
• ISSN: 2238-3603; 1807-0302
• DOI: 10.1007/s40314-023-02334-6

Based on the ideas of the projected matrix splitting technique and the well-known successive overrelaxation (SOR) iteration method, a projected SOR (PSOR) iteration method is studied in this paper for solving a class of vertical linear complementarity problems, where the system matrix is a vertical block matrix of several square sub-blocks with positive diagonal elements. Convergence analyses of the PSOR iteration method are carefully studied when the square sub-blocks and their row-representative matrices are strictly diagonally dominant, irreducibly diagonally dominant and
H
+
-matrices, respectively. At last, two numerical examples are presented. Numerical results indicate that the PSOR method performs much better than some recent proposed projected splitting methods.