1991•Journal of Physics A Mathematical and GeneralRequires access

The method of moments and the Lanczos representation

J R Fletcher

Abstract

Given the moments of the Hamiltonian of a system, the problem is to find a prescription for the matrix elements in the tridiagonal Lanczos representation in a form suitable for numerical calculation. In this letter a sequence of reductions of the moments is described, whereby the redundant information contained in the higher moments is progressively removed, leading to a numerically stable algorithm for the Lanczos matrix elements.

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Key concepts: Tridiagonal matrix, Lanczos resampling, Lanczos algorithm, Mathematics, Hamiltonian (control theory), Representation (politics), Applied mathematics, Method of moments (probability theory)