Rayleigh-Ritz variation method and connected-moments polynomial approach

TL;DR

This paper demonstrates that the connected-moments polynomial approach is equivalent to the Rayleigh-Ritz variation method in Krylov space and compares their effectiveness through numerical tests on an anharmonic oscillator.

Contribution

It establishes the equivalence between the connected-moments polynomial approach and the Rayleigh-Ritz method, providing insights into their relationship and performance.

Findings

Connected-moments polynomial approach is equivalent to Rayleigh-Ritz in Krylov space

Numerical comparison shows similar performance on anharmonic oscillator

Provides a unified perspective on two computational methods

Abstract

We show that the connected-moments polynomial approach proposed recently is equivalent to the well known Rayleigh-Ritz variation method in the Krylov space. We compare the latter with one of the original connected-moments methods by means of a numerical test on an anharmonic oscillator