3 papers
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.NA2025
Efficient Shallow Ritz Method For 1D Diffusion Problems
Zhiqiang Cai, Anastassia Doktorova, Robert D. Falgout +1
This paper studies the shallow Ritz method for solving the one-dimensional diffusion problem. It is shown that the shallow Ritz method improves the order of approximation dramatica…
math.NA2025
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…