Bounds for the condition number of a class of tridiagonal and block tridiagonal matrices
type: Item
instance of: scholarly article
title: Bounds for the condition number of a class of tridiagonal and block tridiagonal matrices
zbMATH Open document ID: 0708.65041
DOI: 10.1007/BF02575732
published in: Calcolo
publication date: 1989-01-01T00:00:00Z
review text: For tridiagonal matrices \(A=\operatorname{Trid}(1,-\gamma_ n,\beta_ n)\) with \(\gamma_ n\neq 0\) for \(n=1,\ldots,N\) and (i) \(4| \beta_ n| \leq | \gamma_ n\gamma_{n+1}|\) for \(1\leq n<N\), the norms \(\| A^{-1}\|_ 1\) are estimated upwards and in the case \(\beta_ n\), \(\gamma_ n>0\) for \(n=1,\ldots,N-1\) also downwards. The bounds depend on the entries of \(A\) only. Upper bounds are also derived in the case that (i) is required only for \(1\le n\le N-2\), in the case \(\| A^{-1}\|_{\infty}\), and in the case of block tridiagonal matrices.
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 15A12
Mathematics Subject Classification ID: 15A60
zbMATH DE Number: 4164031
zbMATH Keywords: condition numbers
zbMATH Keywords: bounds
zbMATH Keywords: block tridiagonal matrices
author: Giuseppe Piazza
author: Donato Trigiante
reviewed by: Lothar Berg
MaRDI profile type: Publication
cites work: Q3996877
cites work: Methods of inverting tridiagonal matrices
cites work: Sulla determinazione della inversa delle matrici tridiagonali e tridiagonali a blicchi
cites work: An Estimate for the Condition Number of a Matrix
cites work: Condition Number Estimation for Sparse Matrices
cites work: Accelerated Iterative Methods for the Solution of Tridiagonal Systems on Parallel Computers
cites work: A Survey of Condition Number Estimation for Triangular Matrices
cites work: Efficient Algorithms for Computing the Condition Number of a Tridiagonal Matrix
cites work: Q3717660
cites work: Theory of difference equations: Numerical methods and applications
cites work: Inversion of tridiagonal matrices
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description: scientific article; zbMATH DE number 4164031