arXiv subjects

Naiyu Jiang

Publications and source records attributed to Naiyu Jiang.

3 recordsLinked to original sources

arXiv2026

On a stochastic column-block bregman method for nonlinear systems

Sparse solution problems play an important role in both signal processing and image restoration. In this paper, we propose a stochastic column-block nonlinear Bregman method for efficiently computing sparse solutions to nonlinear systems. Under certain assumptions, we analyze the convergence of the proposed method and derive an upper bound for its convergence rate. Numerical experiments, including an image recovery problem, are presented to illustrate the efficiency of the proposed method.

math.NA↗

arXiv2025

A stochastic column-block gradient descent method for solving nonlinear systems of equations

In this paper, we propose a new stochastic column-block gradient descent method for solving nonlinear systems of equations. It has a descent direction and holds an approximately optimal step size obtained through an optimization problem. We provide a thorough convergence analysis, and derive an upper bound for the convergence rate of the new method. Numerical experiments demonstrate that the proposed method outperforms the existing ones.

math.NA↗

arXiv2025

On convergence of greedy block nonlinear Kaczmarz methods with momentum

In this paper, for solving nonlinear systems we propose two pseudoinverse-free greedy block methods with momentum by combining the residual-based weighted nonlinear Kaczmarz and heavy ball methods. Without the full column rank assumptions on Jacobi matrices of nonlinear systems, we provide a thorough convergence analysis, and derive upper bounds for the convergence rates of the new methods. Numerical experiments demonstrate that the proposed methods with momentum are much more effective than the existing ones.

math.NA↗