The conditioning of Toeplitz band matrices

DOI10.1016/0895-7177(96)00052-0zbMath0858.65045OpenAlexW2146435055MaRDI QIDQ1921117

Luigi Brugnano, Pierluigi Amodio

Publication date: 11 March 1997

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0895-7177(96)00052-0

zbMATH Keywords

initial value problemszeros of a polynomialinverse matricesboundary value methodsToeplitz band matricesmatrix condition

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical computation of matrix norms, conditioning, scaling (65F35) Numerical computation of solutions to single equations (65H05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Conditioning of matrices (15A12)

Related Items (11)

BS2 methods for semi-linear second order boundary value problems ⋮ Convergence and stability of boundary value methods for ordinary differential equations ⋮ A kind of generalized backward differentiation formulae for solving fractional differential equations ⋮ Preconditioned quasi-compact boundary value methods for space-fractional diffusion equations ⋮ The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimation ⋮ Block boundary value methods for solving Volterra integral and integro-differential equations ⋮ Generalized Adams method for solving fractional delay differential equations ⋮ High-order finite difference schemes for the solution of second-order BVPs ⋮ Fractional convolution quadrature based on generalized Adams methods ⋮ Solving nonlinear second-order delay initial value problems via the adapted generalized Störmer-Cowell methods ⋮ Fast solution of unsymmetric banded Toeplitz systems by means of spectral factorizations and Woodbury's formula

Cites Work

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• Tridiagonal matrices: Invertibility and conditioning
• Theory of difference equations: Numerical methods and applications
• The inverses of Toeplitz band matrices
• Implicite difference methods for initial-boundary value problems
• Exact inverses of certain band matrices
• The Asymptotic Spectra of Banded Toeplitz and Quasi-Toeplitz Matrices
• The Toeplitz Matrices of an Arbitrary Laurent Polynomial.
• Explicit Inversion Formulas for Toeplitz Band Matrices
• Inversion of Toeplitz Band Matrices
• Stability and convergence of boundary value methods for solving ODE
• A boundary value approach to the numerical solution of initial value problems by multistep methos^†
• On the Location of Zeros of Certain Classes of Polynomials with Applications to Numerical Analysis

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