Extended Krylov subspace for parameter dependent systems

DOI10.1016/j.apnum.2010.03.001zbMath1190.65052OpenAlexW2032919707MaRDI QIDQ973089

Valeria Simoncini

Publication date: 28 May 2010

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2010.03.001

zbMATH Keywords

linear systemsnumerical experimentsiterative methodsprojection-type methodsKrylov subspaceparameter-dependent matrix equations

Mathematics Subject Classification ID

Related Items (13)

Monotone convergence of the extended Krylov subspace method for Laplace-Stieltjes functions of Hermitian positive definite matrices ⋮ Computational Methods for Linear Matrix Equations ⋮ A two-sided short-recurrence extended Krylov subspace method for nonsymmetric matrices and its relation to rational moment matching ⋮ On an integrated Krylov-ADI solver for large-scale Lyapunov equations ⋮ Adaptive rational Krylov subspaces for large-scale dynamical systems ⋮ A reflection on the implicitly restarted Arnoldi method for computing eigenvalues near a vertical line ⋮ Massively parallel implementation and approaches to simulate quantum dynamics using Krylov subspace techniques ⋮ A shifted block FOM algorithm with deflated restarting for matrix exponential computations ⋮ A flexible and adaptive simpler GMRES with deflated restarting for shifted linear systems ⋮ Extended and rational Hessenberg methods for the evaluation of matrix functions ⋮ Matrix equation techniques for certain evolutionary partial differential equations ⋮ Functions of rational Krylov space matrices and their decay properties ⋮ Weighted and deflated global GMRES algorithms for solving large Sylvester matrix equations

Uses Software

• Matlab
• SLICOT

Cites Work

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• Extended Arnoldi methods for large low-rank Sylvester matrix equations
• Convergence analysis of the extended Krylov subspace method for the Lyapunov equation
• Krylov subspace methods for projected Lyapunov equations
• Arnoldi methods for large Sylvester-like observer matrix equations, and an associated algorithm for partial spectrum assignment
• An extended block Arnoldi algorithm for large-scale solutions of the continuous-time algebraic Riccati equation
• Model order reduction: Theory, research aspects and applications. Selected papers based on the presentations at the workshop `Model order reduction, coupled problems and optimization', Leiden, The Netherlands, September 19--23, 2005.
• The extended Krylov subspace method and orthogonal Laurent polynomials
• Krylov-subspace methods for the Sylvester equation
• Approximate inverse preconditioning for shifted linear systems
• Restarted full orthogonalization method for shifted linear systems
• Efficient preconditioning for sequences of parametric complex symmetric linear systems
• Iterative system solvers for the frequency analysis of linear mechanical systems
• A rational Lanczos algorithm for model reduction
• Finite element solution of electromagnetic problems over a wide frequency range via the Padé approximation
• A note on the numerical approximate solutions for generalized Sylvester matrix equations with applications
• Dimension reduction of large-scale systems. Proceedings of a workshop, Oberwolfach, Germany, October 19--25, 2003.
• On the numerical solution of \(AX-XB=C\)
• VIBRATIONAL ANALYSIS OF SHIPS WITH COUPLED FINITE AND BOUNDARY ELEMENTS
• Krylov Subspace Methods for Linear Systems with Tensor Product Structure
• A new investigation of the extended Krylov subspace method for matrix function evaluations
• Recent computational developments in Krylov subspace methods for linear systems
• A New Iterative Method for Solving Large-Scale Lyapunov Matrix Equations
• Fast frequency response computation for Rayleigh damping
• Numerical solution of parameter-dependent linear systems
• Stopping Criteria for Rational Matrix Functions of Hermitian and Symmetric Matrices
• Computing $A^\alpha, \log(A)$, and Related Matrix Functions by Contour Integrals
• Extended Krylov Subspaces: Approximation of the Matrix Square Root and Related Functions
• Restarted GMRES for Shifted Linear Systems
• The Solution of Parametrized Symmetric Linear Systems
• Approximation of Large-Scale Dynamical Systems

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