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ON POSITIVE DEFINITE SOLUTIONS OF THE MATRIX EQUATION X + A*XqA = Q(0 < q ≤ 1)

Xiaoyan Yin, Sanyang Liu and Tiexiang Li
Taiwanese Journal of Mathematics
Vol. 16, No. 4 (August 2012), pp. 1391-1407
Stable URL: http://www.jstor.org/stable/taiwjmath.16.4.1391
Page Count: 17
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ON POSITIVE DEFINITE SOLUTIONS OF THE MATRIX EQUATION X + A*X−qA = Q(0 < q ≤ 1)
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Abstract

Abstract Consider the nonlinear matrix equation X + A*X−qA = Q where 0 < q ≤ 1. A new sufficient condition for this equation to have positive definite solution is provided and two iterative methods for the maximal positive definite solution are proposed. Applying the theory of condition number developed by Rice, an explicit expression of the condition number of the maximal positive definite solution is obtained. The theoretical results are illustrated by numerical examples. 2010 Mathematics Subject Classification: 15A24, 65F10, 65H05. Key words and phrases: Nonlinear matrix equation, Positive definite solution, Condition number.

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