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Simultaneous Similarity Reductions for a Pair of Matrices to Condensed Forms

Research paper by Ren-Cang Li, Qiang Ye

Indexed on: 29 Aug '14Published on: 29 Aug '14Published in: Communications in Mathematics and Statistics



Abstract

We present simultaneous reduction algorithms for two (nonsymmetric) matrices \(A\) and \(B\) to upper Hessenberg and lower Hessenberg forms, respectively. One is through the simultaneous similarity reduction and the other is through a Lanczos–Arnoldi-type iteration. The algorithm that uses the Lanczos–Arnoldi-type iteration can be considered as a generalization of both the nonsymmetric Lanczos algorithm and the standard Arnoldi algorithm. We shall also apply our reduction to construct a model reduction for certain kind second-order single-input single-output system. It is proved that the model reduction has the desirable moment matching property.