Backward Perturbation Analysis for the Matrix Equation A~TXA+B~TYB=D |
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| Authors: | Xing-dong Yang Xiu-hong Feng Qing-quan He |
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| Institution: | Xing-dong Yang,Xiu-hong Feng,Qing-quan He Department of Mathematics,Nanjing University of Information Science and Technology,Nanjing 210044,China |
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| Abstract: | Consider the linear matrix equation A
T
XA + B
T
Y B = D, where A,B are n × n real matrices and D symmetric positive semi-definite matrix. In this paper, the normwise backward perturbation bounds for the solution of the
equation are derived by applying the Brouwer fixed-point theorem and the singular value decomposition as well as the property
of Kronecker product. The results are illustrated by two simple numerical examples. |
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| Keywords: | matrix equation backward error approximate solution |
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