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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Efficient computation of the extreme solutions of $X+A^*X^{-1}A=Q$ and $X-A^*X^{-1}A=Q$


Author: Beatrice Meini
Journal: Math. Comp. 71 (2002), 1189-1204
MSC (2000): Primary 15A24; Secondary 65F10, 65H05
Published electronically: November 20, 2001
MathSciNet review: 1898750
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Abstract: We propose a new quadratically convergent algorithm, having a low computational cost per step and good numerical stability properties, which allows the simultaneous approximation of the extreme solutions of the matrix equations $X+A^* X^{-1}A=Q$ and $X-A^*X^{-1}A=Q$. The algorithm is based on the cyclic reduction method.


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Additional Information

Beatrice Meini
Affiliation: Dipartimento di Matematica, Università di Pisa, via Buonarroti 2, 56127 Pisa, Italy
Email: meini@dm.unipi.it

DOI: http://dx.doi.org/10.1090/S0025-5718-01-01368-0
PII: S 0025-5718(01)01368-0
Keywords: Matrix equation, cyclic reduction, block Toeplitz matrix
Received by editor(s): January 25, 2000
Received by editor(s) in revised form: September 19, 2000
Published electronically: November 20, 2001
Article copyright: © Copyright 2001 American Mathematical Society