Deflating irreducible singular M-matrix algebraic Riccati equations

Wei-guo Wang; Wei-chao Wang; Ren-cang Li

doi:10.3934/naco.2013.3.491

Article Contents

2013, Volume 3, Issue 3: 491-518. Doi: 10.3934/naco.2013.3.491

This issue Previous Article Introduction to the theory of splines with an optimal mesh. Linear Chebyshev splines and applications Next Article Approximation of reachable sets using optimal control algorithms

Deflating irreducible singular M-matrix algebraic Riccati equations

1.
School of Mathematical Sciences, Ocean University of China, Qingdao, 266100
2.
Department of Mathematics, University of Texas at Arlington, P.O. Box 19408, Arlington, TX 76019

Received: April 2012

Revised: December 2012

Published: July 2013

Abstract / Introduction Related Papers Cited by

Abstract

A deflation technique is presented for an irreducible singular $M$-matrix Algebraic Riccati Equation (MARE). The technique improves the rate of convergence of a doubling algorithm, especially for an MARE in the critical case for which without deflation the doubling algorithm converges linearly and with deflation it converges quadratically. The deflation also improves the conditioning of the MARE in the critical case and thus enables its minimal nonnegative solution to be computed more accurately.

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Mathematics Subject Classification: Primary: 15A24, 65F30; Secondary: 65H10.

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