Deflating irreducible singular M-matrix algebraic Riccati equations | Zendy

RenCang Li | Zendy; Wei-chao Wang | Zendy; Weiguo Wang | Zendy

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Deflating irreducible singular <em>M</em>-matrix algebraic Riccati equations

Author(s) -

RenCang Li,

Wei-chao Wang,

Weiguo Wang

Publication year - 2013

Publication title -

numerical algebra control and optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.303

H-Index - 20

eISSN - 2155-3289

pISSN - 2155-3297

DOI - 10.3934/naco.2013.3.491

Subject(s) - mathematics , quadratic growth , algebraic riccati equation , deflation , riccati equation , algebraic number , matrix (chemical analysis) , rate of convergence , convergence (economics) , algebraic equation , mathematical analysis , nonlinear system , partial differential equation , physics , computer science , quantum mechanics , monetary policy , channel (broadcasting) , computer network , materials science , monetary economics , economics , composite material , economic growth

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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