标题：A note on computing the generalized inverse <mml:math alttext="$ A^{(2)}_{T,S}$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msubsup><mml:mi>A</mml:mi><mml:mrow><mml:mtext> </mml:mtext><mml:mi>T</mml:mi><mml:mo>,</mml:mo><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mtext> </mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:mrow></mml:math> of a matrix <mml:math alttext="$A$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>A</mml:mi></mml:math>
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2002
卷号：31
DOI：10.1155/S0161171202013169
出版社：Hindawi Publishing Corporation
摘要：The generalized inverse A T,S (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 T,S (2) has been recently developed with the condition
σ (GA| T)⊂(0,∞), 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 T,S (2) are presented if σ(GA|T) is a subset of the open right half-plane and they are extensions of existing computational procedures of A T,S (2), including special cases such as the weighted Moore-Penrose inverse A M,N † and the Drazin inverse AD. Numerical examples are given to illustrate our results.
