On the correspondence between spectra of the operator pencil $A-\lambda B$ and of the operator $B^{-1}A$

TL;DR

This paper explores the relationship between the spectra of symmetric operator pencils and single operators, providing a reduction method and bounds on eigenvalues similar to Rayleigh-Ritz for better spectral analysis.

Contribution

It introduces a reduction of spectral problems for symmetric operator pencils to single operators and derives Rayleigh-Ritz-like eigenvalue bounds.

Findings

Spectral reduction from pencils to single operators.

Rayleigh-Ritz-like eigenvalue bounds established.

Enhanced spectral analysis techniques for symmetric operator pencils.

Abstract

This paper is concerned with the reduction of the spectral problem for symmetric linear operator pencils to a spectral problem for the single operator. Also, a Rayleigh-Ritz-like bounds on eigenvalues of linear operator pencils are obtained.