Decay rates of inverses of banded M-matrices that are near to Toeplitz matrices

DOI10.1016/0024-3795(88)90211-XzbMath0654.15014MaRDI QIDQ1108349

Ben Polman, Victor Eijkhout

Publication date: 1988

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

inverseToeplitz matricespositive definite banded M-matrices

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) Miscellaneous inequalities involving matrices (15A45)

Related Items (16)

Explicit and asymptotic formulas for \(LDM^ t\) factorization of banded Toeplitz matrices ⋮ An L-Banded Approximation to the Inverse of Symmetric Toeplitz Matrices ⋮ Decay bounds for Bernstein functions of Hermitian matrices with applications to the fractional graph Laplacian ⋮ Wavelet sparse approximate inverse preconditioners ⋮ Vectorizable preconditioners for elliptic difference equations in three space dimensions ⋮ Decay Bounds for Functions of Hermitian Matrices with Banded or Kronecker Structure ⋮ The structured distance to singularity of a symmetric tridiagonal Toeplitz matrix ⋮ Localization in Matrix Computations: Theory and Applications ⋮ Non-Toeplitz decay bounds for inverses of Hermitian positive definite tridiagonal matrices ⋮ A probing method for computing the diagonal of a matrix inverse ⋮ Monotone convex sequences and Cholesky decomposition of symmetric Toeplitz matrices ⋮ Inexact Arnoldi residual estimates and decay properties for functions of non-Hermitian matrices ⋮ On some ways of approximating inverses of banded matrices in connection with deriving preconditioners based on incomplete block factorizations ⋮ Analysis of Probing Techniques for Sparse Approximation and Trace Estimation of Decaying Matrix Functions ⋮ Inverse properties of a class of seven-diagonal (near) Toeplitz matrices ⋮ Two-sided bounds on the inverses of diagonally dominant tridiagonal matrices

Cites Work

• Toeplitz matrices with banded inverses
• On approximate factorization methods for block matrices suitable for vector and parallel processors
• Inverses of Matrices $\{a_{ij}\}$ which Satisfy $a_{ij} = 0$ for $j > i+p$.
• Decay Rates for Inverses of Band Matrices

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