Generalized locally Toeplitz sequences: Spectral analysis and applications to discretized partial differential equations
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Publication:1874678
DOI10.1016/S0024-3795(02)00504-9zbMath1028.65109MaRDI QIDQ1874678
Publication date: 25 May 2003
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
orthogonal polynomialseigenvaluesintegral equationsfinite differencessingular valuesspectral distributionToeplitz matricesmultidimensional Szegő formulasToeplitz and locally Toeplitz sequences
Boundary value problems for second-order elliptic equations (35J25) Eigenvalues, singular values, and eigenvectors (15A18) Finite difference methods for boundary value problems involving PDEs (65N06)
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Cites Work
- Unnamed Item
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- Unnamed Item
- On unitarily invariant norms of matrix-valued linear positive operators.
- Asymptotic expansions for pseudodifferential operators on bounded domains
- On the distribution of the singular values of Toeplitz matrices
- On bilinear forms in Gaussian random variables and Toeplitz matrices
- Thin structure of eigenvalue clusters for non-Hermitian Toeplitz matrices
- Szegö's limit theorem: The higher-dimensional matrix case
- Introduction to large truncated Toeplitz matrices
- The rate of convergence of Toeplitz based PCG methods for second order nonlinear boundary value problems
- The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients
- Locally Toeplitz sequences: Spectral properties and applications
- Influence of matrix operations on the distribution of eigenvalues and singular values of Toeplitz matrices
- Spectra of multilevel Toeplitz matrices: Advanced theory via simple matrix relationships
- Extreme singular values and eigenvalues of non-Hermitian block Toeplitz matrices
- Capizzano, Stefano Serra
- Some results on complex Toeplitz eigenvalues
- Asymptotic behavior of block Toeplitz matrices and determinants
- A unifying approach to some old and new theorems on distribution and clustering
- Spectral and structural analysis of high precision finite difference matrices for elliptic operators
- Matrix Analysis
- The Spectral Theory of Toeplitz Operators. (AM-99)
- Fast Preconditioned Conjugate Gradient Algorithms for Wiener–Hopf Integral Equations
- Locally X Matrices, Spectral Distributions, Preconditioning, and Applications
- Superlinear Preconditioners for Finite Differences Linear Systems
- Conjugate Gradient Methods for Toeplitz Systems
- Asymptotic Spectra of Hermitian Block Toeplitz Matrices and Preconditioning Results
- Singular values and eigenvalues of non-Hermitian block Toeplitz matrices
- A note on the asymptotic spectra of finite difference discretizations of second order elliptic partial differential equations
- Distribution results on the algebra generated by Toeplitz sequences: A finite-dimensional approach
- Spectral behavior of matrix sequences and discretized boundary value problems
- Asymptotic zero distribution of orthogonal polynomials with discontinuously varying recurrence coefficients