Bounds for the condition number of a class of tridiagonal and block tridiagonal matrices
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.
scientific article; zbMATH DE number 4164031
scientific article