论文信息 - A preconditioned method for saddle point problems

A preconditioned method for saddle point problems

A preconditioned method for saddle point problems is presented and analyzed. We directly generate an approximation of the inverse matrix, and apply the generated approximation as a preconditioner to some standard iterative solution methods. Moreover, we present a double preconditioned method for special saddle point problems. The method is illustrated by several examples derived from the surface fitting problems. Preliminary numerical results indicate that the method is efficient. AMS Subject Classifications : 65F10, 65N25 Keyword : Saddle Point Problem, Preconditioned Method, Surface Fitting Problem

Kouji Hashimoto | 橋本弘治

[1] O. Axelsson. Iterative solution methods , 1995 .

[2] G. Golub,et al. Inexact and preconditioned Uzawa algorithms for saddle point problems , 1994 .

[3] Xiaojun Chen,et al. On preconditioned Uzawa methods and SOR methods for saddle-point problems , 1998 .

[4] Stephen Roberts,et al. Finite element thin plate splines for surface fitting , 1997 .

[5] Xiaojun Chen,et al. Numerical validation of solutions of saddle point matrix equations , 2003, Numer. Linear Algebra Appl..

[6] Gene H. Golub,et al. An Algebraic Analysis of a Block Diagonal Preconditioner for Saddle Point Systems , 2005, SIAM J. Matrix Anal. Appl..

[7] Anne Greenbaum,et al. Iterative methods for solving linear systems , 1997, Frontiers in applied mathematics.

[8] Owe Axelsson. Eigenvalue Estimates for Preconditioned Saddle Point Matrices , 2003, LSSC.

[9] Apostol T. Vassilev,et al. Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems , 1997 .