Numerical inverting of matrices of high order. II

Abstract

Chapter VIII.Probabilistic estimates for bounds of matrices 8.1 A result of Bargmann, Montgomery and von Neumann.188 8.2 An estimate for the length of a vector.191 8.3 The fundamental lemma.8.4 Some discrete distributions.8.5 Continuation.8.6 Two applications of (8.16).Chapter IX.The error estimates 9.1 Reconsideration of the estimates (6.42)-(6.44)and their consequences.. 9.2 The general A¡.9.3 Concluding evaluation. PrefaceIn an earlier paper,1 to which the present one is a sequel, we derived rigorous error estimates in connection with inverting matrices of high order.In this paper we reconsider the problem from a probabilistic point of view and reassess our critical estimates in this light.Our conclusions are given in Chapter IX and are summarized in §9.3.As in the earlier paper we have here made no effort to obtain optimal numerical estimates.However, we do feel that within the framework of our method our estimates give the correct orders of magnitude.This work has been made possible by the generous support of the Office of