Simultaneous Similarity Reductions for a Pair of Matrices to Condensed Forms
نویسندگان
چکیده
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.
منابع مشابه
Similarity of Families of Matrices An article in CRC Handbook of Linear Algebra
2. Simultaneous similarity of tuples of matrices over C. Problem 1 is notoriously difficult. We show that for the local ring H0 this problem reduces to a Problem 2 for certain kind of matrices. We then discuss certain special cases of Problem 2 as simultaneous similarity of tuples of matrices to upper triangular and diagonal matrices. L-property of pairs of matrices, that discussed next, is clo...
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