Two-sided bounds on the inverses of diagonally dominant tridiagonal matrices

DOI10.1016/S0024-3795(98)10146-5zbMath0951.15005WikidataQ127024628 ScholiaQ127024628MaRDI QIDQ1301308

Reinhard Nabben

Publication date: 14 February 2000

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

zbMATH Keywords

Hadamard product\(M\)-matrixupper and lower boundsinversestridiagonal matricesiterative refinementnonsingular matrixdiagonally dominant tridiagonal matrices

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Miscellaneous inequalities involving matrices (15A45)

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Uses Software

• mctoolbox

Cites Work

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• A theorem on inverses of tridiagonal matrices
• Decay rates of inverses of banded M-matrices that are near to Toeplitz matrices
• On inverses of Hessenberg matrices
• Upper and lower bounds for inverse elements of finite and infinite tridiagonal matrices
• Block Preconditioning for the Conjugate Gradient Method
• Decay Rates for Inverses of Band Matrices
• A Review on the Inverse of Symmetric Tridiagonal and Block Tridiagonal Matrices
• Variational bounds on the entries of the inverse of a matrix
• Inverses of Band Matrices and Local Convergence of Spline Projections
• Decay Rates of the Inverse of Nonsymmetric Tridiagonal and Band Matrices
• On Two-Sided Bounds Related to Weakly Diagonally Dominant M-Matrices with Application to Digital Circuit Dynamics
• On a Finite Difference Analogue of an Elliptic Boundary Problem which is Neither Diagonally Dominant Nor of Non‐negative Type
• Inequalities on the Elements of the Inverse of a Certain Tridiagonal Matrix
• Note on Bounds for Determinants with Dominant Principal Diagonal