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Title of Journal: Numer Algor

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Abbravation: Numerical Algorithms

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Springer US

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DOI

10.1016/0040-6031(83)80277-9

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1572-9265

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Numerical solution to generalized Lyapunov/Stein a

Authors: HungYuan Fan Peter ChangYi Weng Eric KingWah Chu
Publish Date: 2015/04/17
Volume: 71, Issue: 2, Pages: 245-272
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Abstract

We consider the numerical solution of the generalized Lyapunov and Stein equations in mathbb Rn arising respectively from stochastic optimal control in continuous and discretetime Generalizing the Smith method our algorithms converge quadratically and have an On 3 computational complexity per iteration and an On 2 memory requirement For largescale problems when the relevant matrix operators are “sparse” our algorithm for generalized Stein or Lyapunov equations may achieve the complexity and memory requirement of On or similar to that of the solution of the linear systems associated with the sparse matrix operators These efficient algorithms can be applied to Newton’s method for the solution of the rational Riccati equations This contrasts favourably with the naive Newton algorithms of On 6 complexity or the slower modified Newton’s methods of On 3 complexity The convergence and error analysis will be considered and numerical examples provided

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