A symplectic acceleration method for the solution of the algebraic riccati equation on a parallel computer

Wen-Wei Lin*, S. S. You

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We give a cubic acceleration method for improving the current symplectic Jacobi-like algorithm for computing the Hamiltonian-Schur decomposition of a Hamiltonian matrix and finding the positive semidefinite solution of the Riccati equation. The acceleration method can speed up the rate of convergence at the end of the symplectic Jacobi-like process when the norm of the current strictly J-lower triangle has become sufficiently small; it has high parallelism and takes O(n) computational time when implemented on a mesh-connected n × n array processor system. A quantitative analysis of convergence and numerical comparisons of one Jacobi sweep versus one correction step are presented.

Original languageEnglish
Pages (from-to)437-463
Number of pages27
JournalLinear Algebra and Its Applications
Volume188-189
Issue numberC
DOIs
StatePublished - 1 Jan 1993

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