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

DOI10.1016/S0898-1221(97)00074-6zbMath0889.65034OpenAlexW2147129570MaRDI QIDQ1368482

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

Publication date: 2 June 1998

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0898-1221(97)00074-6

zbMATH Keywords

convergencenumerical exampleeigenvaluessymplectic basislarge and sparse Hamiltonian matrixlarge sparse algebraic Riccati equationsshift invert Lanczos algorithm

Mathematics Subject Classification ID

Related Items (13)

Balancing sparse Hamiltonian eigenproblems ⋮ On the conditioning of factors in the SR decomposition ⋮ Electromagnetic field behavior of 3D Maxwell's equations for chiral media ⋮ An invariant subspace method for large-scale algebraic Riccati equation ⋮ The bi-Lebedev scheme for the Maxwell eigenvalue problem with 3D bi-anisotropic complex media ⋮ On the solution of large-scale algebraic Riccati equations by using low-dimensional invariant subspaces ⋮ A structure preserving approximation method for Hamiltonian exponential matrices ⋮ Numerical algorithms for undamped gyroscopic systems ⋮ Approximation of the matrix exponential operator by a structure-preserving block Arnoldi-type method ⋮ A Hamiltonian Krylov-Schur-type method based on the symplectic Lanczos process ⋮ Numerical solution of large‐scale Lyapunov equations, Riccati equations, and linear‐quadratic optimal control problems ⋮ Structured Eigenvalue Problems ⋮ A block \(J\)-Lanczos method for Hamiltonian matrices

Cites Work

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• On Hamiltonian and symplectic Hessenberg forms
• A symplectic method for approximating all the eigenvalues of a Hamiltonian matrix
• On some algebraic problems in connection with general eigenvalue algorithms
• Eigenvalues of perturbed Hermitian matrices
• A Schur method for solving algebraic Riccati equations
• Residual Bounds on Approximate Eigensystems of Nonnormal Matrices
• A Convergence Analysis for Nonsymmetric Lanczos Algorithms
• A Chart of Numerical Methods for Structured Eigenvalue Problems
• Computation of Stable Invariant Subspaces of Hamiltonian Matrices
• A symplectic QR like algorithm for the solution of the real algebraic Riccati equation

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