3 papers
math.NA2026
Structure-Guided Gauss-Newton Method: Linear Advection-Reaction Equation
Zhiqiang Cai, César Herrera
The least-squares neural network (LSNN) method introduced in [5] for linear advection-reaction equations is capable of accurately approximating discontinuous solutions without a pr…
math.NA2026
Convergence Analysis of Block Newton Methods for 1D Shallow Neural Network Approximation
Zhiqiang Cai, Anastassia Doktorova, Robert D. Falgout +1
This paper analyzes local convergence of the block Newton (BN) method introduced in [5, 6] for one-dimensional shallow neural network approximation to functions and diffusion-react…
math.NA2024
Efficient Shallow Ritz Method For 1D Diffusion-Reaction Problems
Zhiqiang Cai, Anastassia Doktorova, Robert D. Falgout +1
This paper studies the shallow Ritz method for solving one-dimensional diffusion-reaction problems. The method is capable of improving the order of approximation for non-smooth pro…