A note on the structured perturbation analysis for the inversion formula of Toeplitz matrices

DOI10.1007/s13160-022-00543-wzbMath1506.15031OpenAlexW4300089449MaRDI QIDQ2111577

Yanyan Li

Publication date: 17 January 2023

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13160-022-00543-w

zbMATH Keywords

fast Fourier transforminvertibilitycirculant matrixstructured perturbation analysisToeplitz matrix inversion

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Theory of matrix inversion and generalized inverses (15A09) Perturbation theory of linear operators (47A55) Roundoff error (65G50) Toeplitz, Cauchy, and related matrices (15B05)

Related Items (2)

Numerical algorithms for corner-modified symmetric Toeplitz linear system with applications to image encryption and decryption ⋮ Fast algorithms for perturbed Toeplitz-plus-Hankel system based on discrete cosine transform and their applications

Cites Work

• Circulant preconditioned iterative methods for peridynamic model simulation
• An approximate inverse preconditioner for Toeplitz systems with multiple right-hand sides
• A circulant preconditioner for fractional diffusion equations
• Algebraic methods for Toeplitz-like matrices and operators
• On inversion of Toeplitz and close to Toeplitz matrices
• The weak and strong stability of algorithms in numerical linear algebra
• A constructive proof of the Gohberg-Semencul formula
• Inversion of Toeplitz matrices with only two standard equations
• On inversion of Toeplitz matrices
• On the reconstruction of Toeplitz matrix inverses from columns
• A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations
• A note on the stability of Toeplitz matrix inversion formulas.
• Circulants, displacements and decompositions of matrices
• The stability of inversion formulas for Toeplitz matrices
• A limited-memory block bi-diagonal Toeplitz preconditioner for block lower triangular Toeplitz system from time-space fractional diffusion equation
• Fast iterative method with a second-order implicit difference scheme for time-space fractional convection-diffusion equation
• A note on inversion of Toeplitz matrices
• Hartley Transform Representations of Symmetric Toeplitz Matrix Inverses with Application to Fast Matrix-Vector Multiplication
• A Stabilized Superfast Solver for Nonsymmetric Toeplitz Systems
• Shift-Invert Arnoldi Approximation to the Toeplitz Matrix Exponential
• A Weakly Stable Algorithm for Padé Approximants and the Inversion of Hankel Matrices
• An inexact shift‐and‐invert Arnoldi algorithm for Toeplitz matrix exponential
• Stability of Methods for Solving Toeplitz Systems of Equations
• A new Toeplitz inversion formula, stability analysis and the value
• Conjugate Gradient Methods for Toeplitz Systems
• Fast algorithms for high-order numerical methods for space-fractional diffusion equations
• Preconditioners for Symmetrized Toeplitz and Multilevel Toeplitz Matrices
• A class of second order difference approximations for solving space fractional diffusion equations
• An Algorithm for the Inversion of Finite Toeplitz Matrices
• An Inexact Shift-and-Invert Arnoldi Algorithm for Large Non-Hermitian Generalised Toeplitz Eigenproblems
• An Introduction to Iterative Toeplitz Solvers
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A note on the structured perturbation analysis for the inversion formula of Toeplitz matrices