# A homogeneous Rayleigh quotient with applications in gradient methods

arXiv: https://arxiv.org/abs/2206.13457 · HTML: https://mlsanity.com/paper/2206.13457/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2022.

## Built on by (most cited first, 1 of 1)

- [Smoothness Errors in Dynamics Models and How to Avoid Them](https://mlsanity.com/paper/2602.05352/) (2026)

## Abstract (arXiv)

Given an approximate eigenvector, its (standard) Rayleigh quotient and harmonic Rayleigh quotient are two well-known approximations of the corresponding eigenvalue. We propose a new type of Rayleigh quotient, the homogeneous Rayleigh quotient, and analyze its sensitivity with respect to perturbations in the eigenvector. Furthermore, we study the inverse of this homogeneous Rayleigh quotient as stepsize for the gradient method for unconstrained optimization. The notion and basic properties are also extended to the generalized eigenvalue problem.