On the explicit inverse and conditioning of a tridiagonal matrix
Riaz A. Usmani · International Journal of Computer Mathematics · 1992
The expressions for the elements of the inverse of the tridiagonal matrix P n (x y) = [P ij ] so that P ii = 1P i. i+1 = − y, P i+1,i = −x, are obtained. Employing these expressions, we compute which is required in proving that the matrix P n (x y) is well-conditioned if x ≥ 0, y ≥ 0, x + y ≤ 1. Similar results are obtained for some related tridiagonal matrices as well. An application from two-point boundary value problems is briefly discussed to show the usefulness of in proving the convergence of a finite difference method.