8 papers
Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop
Noah Amsel, Yves Baumann, Paul Beckman +36
This document presents a series of open questions arising in matrix computations, i.e., the numerical solution of linear algebra problems. It is a result of working groups at the w…
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…
Nodal Coarsening and Sparse Ideal Interpolation for H(curl) Problems in Algebraic Multigrid
Taoli Shen, James Brannick, Robert Falgout +2
We propose a sparse interpolation construction and a practical coarsening algorithm for the algebraic multigrid (AMG) method, tailored towards H(curl). Building on the generalized…
Parallel-in-time solution of scalar nonlinear conservation laws
O. A. Krzysik, H. De Sterck, R. D. Falgout +1
We consider the parallel-in-time solution of scalar nonlinear conservation laws in one spatial dimension. The equations are discretized in space with a conservative finite-volume m…
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…
Parallel-in-time solution of hyperbolic PDE systems via characteristic-variable block preconditioning
O. A. Krzysik, H. De Sterck, R. D. Falgout +1
We consider the parallel-in-time solution of hyperbolic partial differential equation (PDE) systems in one spatial dimension, both linear and nonlinear. In the nonlinear setting, t…