Circulant and skew-circulant preconditioners for skew-Hermitian type Toeplitz systems

DOI10.1007/BF01933178zbMath0743.65026OpenAlexW2028933557MaRDI QIDQ1182617

Xiao-qing Jin, Raymond Honfu Chan

Publication date: 28 June 1992

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01933178

zbMATH Keywords

preconditioned conjugate gradient methodsNumerical examplesSuperlinear convergencediscretization of hyperbolic equationsskew-circulant preconditionersskew-Hermitian Toeplitz matrices

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items

The inverses and eigenpairs of tridiagonal Toeplitz matrices with perturbed rows ⋮ Determinants and inverses of perturbed periodic tridiagonal Toeplitz matrices ⋮ The explicit identities for spectral norms of circulant-type matrices involving binomial coefficients and harmonic numbers ⋮ Isomorphic operators and functional equations for the skew-circulant algebra ⋮ On skew circulant type matrices involving any continuous Fibonacci numbers ⋮ Optimal backward perturbation analysis for the block skew circulant linear systems with skew circulant blocks ⋮ Determinant and inverse of a Gaussian Fibonacci skew-Hermitian Toeplitz matrix ⋮ Explicit inverse matrices of Tribonacci skew circulant type matrices ⋮ Analysis of the structured perturbation for the BSCCB linear system ⋮ Circulant preconditioners for second order hyperbolic equations ⋮ Jackson's theorem and circulant preconditioned Toeplitz systems ⋮ On optimal backward perturbation analysis for the linear system with skew circulant coefficient matrix ⋮ INVERSES AND EIGENPAIRS OF TRIDIAGONAL TOEPLITZ MATRIX WITH OPPOSITE-BORDERED ROWS ⋮ The determinants, inverses, norm, and spread of skew circulant type matrices involving any continuous Lucas numbers ⋮ ON INVERSES AND EIGENPAIRS OF PERIODIC TRIDIAGONAL TOEPLITZ MATRICES WITH PERTURBED CORNERS ⋮ On \(k\)-step CSCS-based polynomial preconditioners for Toeplitz linear systems with application to fractional diffusion equations

Uses Software

• CGS

Cites Work

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• The circulant operator in the Banach algebra of matrices
• A Proposal for Toeplitz Matrix Calculations
• CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
• Toeplitz Equations by Conjugate Gradients with Circulant Preconditioner
• On the Solution of Certain Skew Symmetric Linear Systems
• Circulant Preconditioners for Hermitian Toeplitz Systems

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