標題: The shift-inverted J-Lanczos algorithm for the numerical solutions of large sparse algebraic Riccati equations
作者: Ferng, WR
Lin, WW
Wang, CS
應用數學系
Department of Applied Mathematics
關鍵字: Riccati equation;Hamiltonian matrix;J-Lanczos algorithm;J-tridiagonalization;sympletic matrix;SR factorization
公開日期: 1-May-1997
摘要: The goal of solving an algebraic Riccati equation is to find the stable invariant subspace corresponding to all the eigenvalues lying in the open left-half plane. The purpose of this paper is to propose a structure-preserving Lanczos-type algorithm incorporated with shift and invert techniques, named shift-inverted J-Lanczos algorithm, for computing the stable invariant subspace for large sparse Hamiltonian matrices. The algorithm is based on the J-tridiagonalization procedure of a Hamiltonian matrix using symplectic similarity transformations. We give a detailed analysis on the convergence behavior of the J-Lanczos algorithm and present error bound analysis and Paige-type theorem. Numerical results for the proposed algorithm applied to a practical example arising from the position and velocity control for a string of high-speed vehicles are reported.
URI: http://hdl.handle.net/11536/561
ISSN: 0898-1221
期刊: COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume: 33
Issue: 10
起始頁: 23
結束頁: 40
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  1. A1997XJ00100003.pdf