Preconditioning for a class of spectral differentiation matrices

DOI10.1007/s10915-004-4794-4zbMath1080.65113OpenAlexW2146745011MaRDI QIDQ2576787

Manfred R. Trummer, Ronald D. Haynes, Weiming Cao

Publication date: 14 December 2005

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-004-4794-4

zbMATH Keywords

convergenceNewton's methodpseudospectral methoddynamical systemsnumerical examplesbifurcationfast Fourier transformvan der Pol oscillatorinvariant torusspectral collocationfirst-order partial differential equationsPreconditionersiterative methods for nonsymmetric systems

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Linear first-order PDEs (35F05) Computational methods for bifurcation problems in dynamical systems (37M20) Numerical bifurcation problems (65P30)

Related Items (1)

Equivalent operator preconditioning for elliptic problems

Uses Software

• Eigtool

Cites Work

• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• A semi-circulant preconditioner for the convection-diffusion equation
• Spectral methods in computing invariant tori
• Block iterations and compactification for periodic block dominant systems associated to invariant tori approximation
• On the theory of equivalent operators and application to the numerical solution of uniformly elliptic partial differential equations
• The Adaptive Verlet Method
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• Block M-Matrices and Computation of Invariant Tori
• Variants of BICGSTAB for Matrices with Complex Spectrum
• Solution of the Systems Associated with Invariant Tori Approximation. II: Multigrid Methods
• The Best Circulant Preconditioners for Hermitian Toeplitz Systems
• Any Nonincreasing Convergence Curve is Possible for GMRES
• Numerical Calculation of Invariant Tori
• Efficient preconditioning of linear systems arising from the discretization of hyperbolic conservation laws

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