The shift-inverted J-Lanczos algorithm for the numerical solutions of large sparse algebraic Riccati equations

W. R. Ferng, Wen-Wei Lin, Chern Shuh Wang

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)23-40
Number of pages18
JournalComputers and Mathematics with Applications
Volume33
Issue number10
DOIs
StatePublished - 1 Jan 1997

Keywords

  • Hamiltonian matrix
  • J-Lanczos algorithm
  • J-tridiagonalization
  • Riccati equation
  • SR factorization
  • Sympletic matrix

Fingerprint Dive into the research topics of 'The shift-inverted J-Lanczos algorithm for the numerical solutions of large sparse algebraic Riccati equations'. Together they form a unique fingerprint.

Cite this