PERTURBATION ANALYSIS OF HILBERT LINEAR SYSTEMS ARISING IN APPLICATIONS

Abstract

Perturbation analysis of Hilbert linear systems arising in applications is reported. This paper shows the impact of error bound in relation to the perturbation of the linear system. The goal is to bound the relative error of A𝒙 = b when both the right-hand side (RHS) vector b and the coefficient matrix A are perturbed slightly and to determine the relevance of small residual vector. We considered a Hilbert system for the conditioning due to its unique sensitivity to perturbation. From our numerical results ran on MATLAB version 7.01, the condition number of the Hilbert matrix gets larger as size (n) of the matrix increases. We also showed that small residual does not necessarily mean that the approximate solution is ‘close’ to the exact solution and again small residual does not imply a small error vector of the linear system.