A DEFLATION APPROACH FOR LARGE-SCALE LUR%26apos;E EQUATIONS

作者：Poloni Federico^*; Reis Timo

来源：SIAM Journal on Matrix Analysis and Applications, 2012, 33(4): 1339-1368.

DOI：10.1137/120861679

• Lur%26apos
• e equations
• Riccati equations
• deflating subspaces
• even matrix pencils
• Newton-Kleinman method
• ADI iteration

We present an approach to the determination of the stabilizing solution of Lur%26apos;e matrix equations. We show that the knowledge of a certain deflating subspace of an even matrix pencil may lead to Lur%26apos;e equations which are defined on some subspace, the so-called %26quot;projected Lur%26apos;e equations.%26quot; These projected Lur%26apos;e equations are shown to be equivalent to projected Riccati equations, if the deflating subspace contains the subspace corresponding to infinite eigenvalues. This result leads to a novel numerical algorithm that basically consists of two steps. First we determine the deflating subspace corresponding to infinite eigenvalues using an algorithm based on the so-called %26quot;neutral Wong sequences,%26quot; which requires a moderate number of kernel computations; then we solve the resulting projected Riccati equations. Altogether this method can deliver solutions in low-rank factored form, it is applicable for large-scale Lur%26apos;e equations and exploits possible sparsity of the matrix coefficients.

• 出版日期2012