Upper and lower bounds for inverse elements of finite and infinite tridiagonal matrices

DOI10.1016/0024-3795(95)00113-1zbMath0862.65015OpenAlexW2078221154MaRDI QIDQ2564962

Chuanxiang Ji, Pappur N. Shivakumar

Publication date: 25 May 1997

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

Full work available at URL: https://doi.org/10.1016/0024-3795(95)00113-1

zbMATH Keywords

upper and lower boundsrecurrence relationsBessel functionsMathieu functionsinverse elementsblock tridiagonal infinite systemsinfinity normstridiagonal diagonally dominant matrices

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Miscellaneous inequalities involving matrices (15A45) Computation of special functions and constants, construction of tables (65D20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Direct numerical methods for linear systems and matrix inversion (65F05) Lamé, Mathieu, and spheroidal wave functions (33E10)

Related Items (9)

On inverses of infinite Hessenberg matrices ⋮ On the finite section method for computing exponentials of doubly-infinite skew-Hermitian matrices ⋮ Estimates for the inverse elements of tridiagonal matrices ⋮ Improved bounds for the inverses of diagonally dominant tridiagonal matrices ⋮ Some improvements for two-sided bounds on the inverse of diagonally dominant tridiagonal matrices ⋮ On the inverses of general tridiagonal matrices ⋮ A review of infinite matrices and their applications ⋮ Two-sided bounds on the inverses of diagonally dominant tridiagonal matrices ⋮ Matrix computations with the Omega calculus

Cites Work

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• Eigenvalues for infinite matrices
• Estimates for the inverse of tridiagonal matrices arising in boundary- value problems
• An iterative method with truncation for infinite linear systems
• A lower bound for the smallest singular value of a matrix
• Linear equations in infinite matrices
• A fast parallel algorithm for the solution of tridiagonal linear systems
• Inequalities on the Elements of the Inverse of a Certain Tridiagonal Matrix
• Note on Bounds for Determinants with Dominant Principal Diagonal

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