# Inexact Gauss-Newton methods with matrix approximation by sampling for nonlinear least-squares and systems

arXiv: https://arxiv.org/abs/2310.05501 · HTML: https://mlsanity.com/paper/2310.05501/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Oct 2023.

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

- [On the Convergence Behavior of Preconditioned Gradient Descent Toward the Rich Learning Regime](https://mlsanity.com/paper/2601.03162/) (2026)

## Abstract (arXiv)

We develop and analyze stochastic inexact Gauss-Newton methods for nonlinear least-squares problems and for nonlinear systems ofequations. Random models are formed using suitable sampling strategies for the matrices involved in the deterministic models. The analysis of the expected number of iterations needed in the worst case to achieve a desired level of accuracy in the first-order optimality condition provides guidelines for applying sampling and enforcing, with minora fixed probability, a suitable accuracy in the random approximations. Results of the numerical validation of the algorithms are presented.