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.
|Number of pages||15|
|Journal||Communications in Mathematics and Statistics|
|State||Published - Jun 1 2014|
Bibliographical noteFunding Information:
Acknowledgments Research of R. Li is supported in part by NSF grants DMS-1115834 and DMS-1317330, and a Research Gift Grant from Intel Corporation. Research of Q. Ye is supported in part by NSF Grants DMS–1318633 and DMS-1317424.
© 2014, School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag Berlin Heidelberg.
- Krylov subspace method
- Lanczos–Arnoldi iteration
- Model reduction
- Simultaneous reductions
ASJC Scopus subject areas
- Statistics and Probability
- Computational Mathematics
- Applied Mathematics