Showing papers by "Zhong-Zhi Bai published in 2006"

Optimal Parameter in Hermitian and Skew-Hermitian Splitting Method for Certain Two-by-Two Block Matrices

Abstract: The optimal parameter of the Hermitian/skew-Hermitian splitting (HSS) iteration method for a real two-by-two linear system is obtained. The result is used to determine the optimal parameters for linear systems associated with certain two-by-two block matrices and to estimate the optimal parameters of the HSS iteration method for linear systems with n-by-n real coefficient matrices. Numerical examples are given to illustrate the results.

Iterative orthogonal direction methods for Hermitian minimum norm solutions of two consistent matrix equations

Abstract: The consistent conditions and the general expressions about the Hermitian solutions of the linear matrix equations AXB=C and (AX, XB)=(C, D) are studied in depth, where A, B, C and D are given matrices of suitable sizes. The Hermitian minimum F-norm solutions are obtained for the matrix equations AXB=C and (AX, XB)=(C, D) by Moore–Penrose generalized inverse, respectively. For both matrix equations, we design iterative methods according to the fundamental idea of the classical conjugate direction method for the standard system of linear equations. Numerical results show that these iterative methods are feasible and effective in actual computations of the solutions of the above-mentioned two matrix equations. Copyright © 2006 John Wiley & Sons, Ltd.

Alternately linearized implicit iteration methods for the minimal nonnegative solutions of the nonsymmetric algebraic Riccati equations

Abstract: For the non-symmetric algebraic Riccati equations, we establish a class of alternately linearized implicit (ALI) iteration methods for computing its minimal non-negative solutions by technical combination of alternate splitting and successive approximating of the algebraic Riccati operators. These methods include one iteration parameter, and suitable choices of this parameter may result in fast convergent iteration methods. Under suitable conditions, we prove the monotone convergence and estimate the asymptotic convergence factor of the ALI iteration matrix sequences. Numerical experiments show that the ALI iteration methods are feasible and effective, and can outperform the Newton iteration method and the fixed-point iteration methods. Besides, we further generalize the known fixed-point iterations, obtaining an extensive class of relaxed splitting iteration methods for solving the non-symmetric algebraic Riccati equations. Copyright © 2006 John Wiley & Sons, Ltd.

A modified damped Newton method for linear complementarity problems

Abstract: We present a modified damped Newton method for solving large sparse linear complementarity problems, which adopts a new strategy for determining the stepsize at each Newton iteration The global convergence of the new method is proved when the system matrix is a nondegenerate matrix We then apply the matrix splitting technique to this new method, deriving an inexact splitting method for the linear complementarity problems The global convergence of the resulting inexact splitting method is proved, too Numerical results show that the new methods are feasible and effective for solving the large sparse linear complementarity problems

Two-step iterative methods for solving the stationary convection-diffusion equation with a small parameter at the highest derivative on a uniform grid

Abstract: A stationary convection-diffusion problem with a small parameter multiplying the highest derivative is considered. The problem is discretized on a uniform rectangular grid by the central-difference scheme. A new class of two-step iterative methods for solving this problem is proposed and investigated. The convergence of the methods is proved, optimal iterative methods are chosen, and the rate of convergence is estimated. Numerical results are presented that show the high efficiency of the methods.