Showing papers by "Zhong-Zhi Bai published in 2016"

On SSOR‐like preconditioners for non‐Hermitian positive definite matrices

Abstract: We construct, analyze and implement SSOR-like preconditioners for non-Hermitian positive definite system of linear equations when its coefficient matrix possesses either a dominant Hermitian part or a dominant skew-Hermitian part. We derive tight bounds for eigenvalues of the preconditioned matrices and obtain convergence rates of the corresponding SSOR-like iteration methods as well as the corresponding preconditioned GMRES iteration methods. Numerical implementations show that Krylov subspace iteration methods such as GMRES, when accelerated by the SSOR-like preconditioners, are efficient solvers for these classes of non-Hermitian positive definite linear systems.

Rigorous convergence analysis of alternating variable minimization with multiplier methods for quadratic programming problems with equality constraints

Abstract: We discuss unique solvability of the equality-constraint quadratic programming problem, establish a class of preconditioned alternating variable minimization with multiplier (PAVMM) methods for iteratively computing its solution, and demonstrate asymptotic convergence property of these PAVMM methods. We also discuss an algebraic derivation of the PAVMM method by making use of matrix splitting, which reveals that the PAVMM method is actually a modified block Gauss–Seidel iteration method for solving the augmented Lagrangian linear system resulting from the weighted Lagrangian function with respect to the equality-constraint quadratic programming problem.