Bounds for the Error of Linear Systems of Equations Using the Theory of Moments

摘要

Consider the system of linear equations Ax = b where A is an nxn real symmetric, positive definite matrix and b is a known vector. Suppose one is given an approximation to x, xi, and one wishes to determine upper and lower bounds for / x - xi/ where /.../ indicates the euclidean norm. It is shown how to construct a sequence of upper and lower bounds for / x - xi/ using the theory of moments.