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  • 标题:A note on computing the generalized inverse <mml:math alttext="$ A^{(2)}_{T,S}$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msubsup><mml:mi>A</mml:mi><mml:mrow><mml:mtext>&#8201;</mml:mtext><mml:mi>T</mml:mi><mml:mo>,</mml:mo><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mtext>&#8201;</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:mrow></mml:math> of a matrix <mml:math alttext="$A$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>A</mml:mi></mml:math>
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  • 作者:Xiezhang Li ; Yimin Wei
  • 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&#8201;T,S&#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&#8201;T,S&#8201;(2) has been recently developed with the condition &#963;&#8201;(GA|&#8201;T)&#8834;(0,&#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&#8201;T,S&#8201;(2) are presented if &#963;(GA|T) is a subset of the open right half-plane and they are extensions of existing computational procedures of A&#8201;T,S&#8201;(2), including special cases such as the weighted Moore-Penrose inverse A&#8201;M,N&#8201;&#8224; and the Drazin inverse AD. Numerical examples are given to illustrate our results.
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