# American Institute of Mathematical Sciences

2013, 3(3): 491-518. doi: 10.3934/naco.2013.3.491

## Deflating irreducible singular M-matrix algebraic Riccati equations

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

Received  April 2012 Revised  December 2012 Published  July 2013

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.
Citation: Wei-guo Wang, Wei-chao Wang, Ren-cang Li. Deflating irreducible singular M-matrix algebraic Riccati equations. Numerical Algebra, Control & Optimization, 2013, 3 (3) : 491-518. doi: 10.3934/naco.2013.3.491
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