Related papers: A Parallel and Scalable Iterative Solver for Seque…
A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces. Convergence is established for a wide class of coupling schemes. Unlike classical alternating algorithms, which are limited to two…
Nonlinear eigenvalue problems with eigenvector nonlinearities (NEPv) are algebraic eigenvalue problems whose matrix depends on the eigenvector. Applications range from computational quantum mechanics to machine learning. Due to its…
We introduce AutoSpec, a neural network framework for discovering iterative spectral algorithms for large-scale numerical linear algebra and numerical optimization. Our self-supervised models adapt to input operators using coarse spectral…
We propose efficient parallel algorithms and implementations on shared memory architectures of LU factorization over a finite field. Compared to the corresponding numerical routines, we have identified three main difficulties specific to…
Exponential time integrators have been applied successfully in several physics-related differential equations. However, their application in hyperbolic systems with absorbing boundaries, like the ones arising in seismic imaging, still lacks…
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 method using weighted essentially non-oscillatory (WENO)…
Given samples of a real or complex-valued function on a set of distinct nodes, the traditional linear Chebyshev approximation is to compute the best minimax approximation on a prescribed linear functional space. Lawson's iteration is a…
Accurate and efficient computation of Floquet multipliers and subspaces is essential for analyzing limit cycle in dynamical systems and periodic steady state in Radio Frequency simulation. This problem is typically addressed by solving a…
We propose a novel method for the efficient and accurate iterative solution of frequency domain integral equations (IEs) that are used for large/multi-scale electromagnetic scattering problems. The proposed method uses a novel…
We propose a novel iterative algorithm for solving a large sparse linear system. The method is based on the EM algorithm. If the system has a unique solution, the algorithm guarantees convergence with a geometric rate. Otherwise,…
This paper introduces an efficient algorithm for finding the dominant generalized eigenvectors of a pair of symmetric matrices. Combining tools from approximation theory and convex optimization, we develop a simple scalable algorithm with…
Matrix computations, especially iterative PDE solving (and the sparse matrix vector multiplication subproblem within) using conjugate gradient algorithm, and LU/Cholesky decomposition for solving system of linear equations, form the kernel…
In the recent paper [Duff I. et al, SIAM J. Sci. Comp., 37(3) (2015), A1248-A1269] the authors proposed an interesting procedure for the parallel solution of large, sparse consistent linear systems of equations. In this respect, according…
We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which is a provably convergent, second order incremental algorithm for solving large-scale partially separable optimization problems. The algorithm is based on a local…
Chebyshev polynomials have shown significant promise as an efficient tool for both classical and quantum neural networks to solve linear and nonlinear differential equations. In this work, we adapt and generalize this framework in a quantum…
We propose a flexible machine-learning framework for solving eigenvalue problems of diffusion operators in moderately large dimension. We improve on existing Neural Networks (NNs) eigensolvers by demonstrating our approach ability to…
We consider the problem of low-rank approximation of massive dense non-negative tensor data, for example to discover latent patterns in video and imaging applications. As the size of data sets grows, single workstations are hitting…
The key innovation in this paper is an open-source, high-performance iterative solver for high contrast, strongly anisotropic elliptic partial differential equations implemented within dune-pdelab. The iterative solver exploits a robust,…
We introduce PHEW (Parallel HiErarchical Watershed), a new segmentation algorithm to detect structures in astrophysical fluid simulations, and its implementation into the adaptive mesh refinement (AMR) code ramses. PHEW works on the density…
Optimally hybrid numerical solvers were constructed for massively parallel generalized eigenvalue problem (GEP).The strong scaling benchmark was carried out on the K computer and other supercomputers for electronic structure calculation…