J4 ›› 2009, Vol. 44 ›› Issue (10): 30-35.

• Articles • Previous Articles     Next Articles

Preconditioned simultaneous displacement(PSD) method for rank deficient  linear systems

 YUE Jiang, CHANG Da-Wei   

  1. College of Mathematics and Information Science, Shaanxi Normal University,Xi an 710062, Shaanxi, China
  • Received:2009-03-16 Online:2009-10-16 Published:2009-12-07

Abstract:

The rank deficient linear systemÂx=b  is augmented to a block 4×4 linear system Âη=b´, where A is a square matrix, then A is split with PSD subproper splitting. The necessary and sufficient condition for the PSD method being semiconvergent is obtained. Finally a method is provided to compute the least square solution of minimal norm to ]Ax=b and exmamples are given to illustrate the process, whereA∈Cm×nb∈Cm,b´∈C m+n

Key words: PSD splitting; Semiconvergent; Least square solution; Moore-Penrose generalized inverse

CLC Number: 

  • Q241.6
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