A systolic algorithm for Riccati and Lyapunov equations

DOI10.1007/BF02551818zbMath0675.65032OpenAlexW2043227016MaRDI QIDQ1122310

J.-P. Charlier, Paul Van Dooren

Publication date: 1989

Published in: MCSS. Mathematics of Control, Signals, and Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02551818

zbMATH Keywords

algebraic Riccati equationLyapunov matrix equationparallel algorithmfactorizationsHamiltonian matrixsystolic algorithmrecursive matrix sign function method

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Synthesis problems (93B50) Parallel numerical computation (65Y05)

Related Items (max. 100)

The matrix sign decomposition and its relation to the polar decomposition ⋮ Trace norm bounds for stable Lyapunov operators ⋮ Parallel algorithms for algebraic Riccati equations ⋮ Convex invertible cones of matrices -- a unified framework for the equations of Sylvester, Lyapunov and Riccati

Uses Software

• Algorithm 432

Cites Work

• A Schur decomposition for Hamiltonian matrices
• A triangular processor array for computing singular values
• Solving the algebraic Riccati equation with the matrix sign function
• Linear algebra on high performance computers
• Inertia and eigenvalue relations between symmetrized and symmetrizing matrices for the real and the general field case
• A generalization of the matrix-sign-function solution for algebraic Riccati equations
• Data-flow algorithms for parallel matrix computation
• A Schur method for solving algebraic Riccati equations
• On the numerical solution of the discrete-time algebraic Riccati equation
• A Generalized Eigenvalue Approach for Solving Riccati Equations
• Numerical Solution of the Stable, Non-negative Definite Lyapunov Equation Lyapunov Equation
• Second-order convergent algorithms for the steady-state Riccati equation†
• Newton's Method for the Matrix Square Root
• A Note on Downdating the Cholesky Factorization
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A systolic algorithm for Riccati and Lyapunov equations