Filtered Rayleigh-Ritz is all you need
- MIT
- Fermilab
- UC, Berkeley; LBNL, NSD
Recent work has shown that the (block) Lanczos algorithm can be used to extract approximate energy spectra and matrix elements from (matrices of) correlation functions in quantum field theory, and identified exact coincidences between Lanczos analysis methods and others. In this work, we note another coincidence: the Lanczos algorithm is equivalent to the well-known Rayleigh-Ritz method applied to Krylov subspaces. Rayleigh-Ritz provides optimal eigenvalue approximations within subspaces; we find that spurious-state filtering allows these optimality guarantees to be retained in the presence of statistical noise. We explore the relation between Lanczos and Prony's method, their block generalizations, generalized pencil of functions (GPOF), and methods based on the generalized eigenvalue problem (GEVP), and find they all fall into a larger "Prony-Ritz equivalence class", identified as all methods which solve a finite-dimensional spectrum exactly given sufficient correlation function (matrix) data. This equivalence allows simpler and more numerically stable implementations of (block) Lanczos analyses.
- Research Organization:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States); MIT; Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); UC, Berkeley
- Sponsoring Organization:
- US Department of Energy
- DOE Contract Number:
- 89243024CSC000002
- OSTI ID:
- 2549341
- Report Number(s):
- FERMILAB-PUB-25-0131-T; MIT-CTP/5849; oai:inspirehep.net:2902781; arXiv:2503.17357
- Journal Information:
- No journal information, Journal Name: No journal information
- Country of Publication:
- United States
- Language:
- English
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