A note on computing the generalized inverse of a matrix

作者:Xiezhang Li; Yimin Wei
来源:International Journal of Mathematics and Mathematical Sciences, 2002.
DOI:10.1155/s0161171202013169

摘要

The generalized inverse A%26#8201;T,S%26#8201;(2) of a matrix A is a {2}-inverse of A with the prescribed range T and null space S. A representation for the generalized inverse A%26#8201;T,S%26#8201;(2) has been recently developed with the condition %26#963;%26#8201;(GA|%26#8201;T)%26#8834;(0,%26#8734;), where G is a matrix with R(G)=T andN(G)=S. In this note, we remove the above condition. Three types of iterative methods for A%26#8201;T,S%26#8201;(2) are presented if %26#963;(GA|T) is a subset of the open right half-plane and they are extensions of existing computational procedures of A%26#8201;T,S%26#8201;(2), including special cases such as the weighted Moore-Penrose inverse A%26#8201;M,N%26#8201;%26#8224; and the Drazin inverse AD. Numerical examples are given to illustrate our results.

  • 出版日期2002

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