A new subspace iteration method for the algebraic Riccati equation |
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Authors: | Yiding Lin Valeria Simoncini |
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Affiliation: | 1. School of Mathematical Sciences, Xiamen University, Xiamen, China;2. Dipartimento di Matematica, Università di Bologna, Bologna, Italy |
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Abstract: | We consider the numerical solution of the continuous algebraic Riccati equation A*X + XA ? XFX + G = 0, with F = F*,G = G* of low rank and A large and sparse. We develop an algorithm for the low‐rank approximation of X by means of an invariant subspace iteration on a function of the associated Hamiltonian matrix. We show that the sought‐after approximation can be obtained by a low‐rank update, in the style of the well known Alternating Direction Implicit (ADI) iteration for the linear equation, from which the new method inherits many algebraic properties. Moreover, we establish new insightful matrix relations with emerging projection‐type methods, which will help increase our understanding of this latter class of solution strategies. Copyright © 2014 John Wiley & Sons, Ltd. |
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Keywords: | Riccati equation ADI rational Krylov subspace invariant subspace iteration |
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