Related papers: A Parallel and Scalable Iterative Solver for Seque…
This paper presents our work on designing scalable linear solvers for large-scale reservoir simulations. The main objective is to support implementation of parallel reservoir simulators on distributed-memory parallel systems, where MPI…
Sequences of parametrized Lyapunov equations can be encountered in many application settings. Moreover, solutions of such equations are often intermediate steps of an overall procedure whose main goal is the computation of…
Extreme and isolated eigenvalues are known to be harmful to the convergence of an iterative solver. These eigenvalues can be produced by strong heterogeneity in the underlying physics. We can improve the quality of the spectrum by…
The advent of large aperture arrays, such as the ones currently under construction for the SKA project, allows for observing the Universe in the radio-spectrum at unprecedented resolution and sensitivity. To process the enormous amounts of…
In this paper, we focus on solving a sequence of linear systems with an identical (or similar) coefficient matrix. For this type of problems, we investigate the subspace correction and deflation methods, which use an auxiliary matrix…
In this work, we consider alternative discretizations for PDEs which use expansions involving integral operators to approximate spatial derivatives. These constructions use explicit information within the integral terms, but treat boundary…
Matrix diagonalization is almost always involved in computing the density matrix needed in quantum chemistry calculations. In the case of modest matrix sizes ($\lesssim$ 5000), performance of traditional dense diagonalization algorithms on…
It is known that the statistical properties of the spectrum provide an essential characterization of quantum chaos. The computation of a large group of interior eigenvalues at the middle spectrum is thus an important problem for quantum…
Large graphs commonly appear in social networks, knowledge graphs, recommender systems, life sciences, and decision making problems. Summarizing large graphs by their high level properties is helpful in solving problems in these settings.…
In this study linear and nonlinear higher order singularly perturbed problems are examined by a numerical approach, the differential quadrature method. Here, the main idea is using Chebyshev polynomials to acquire the weighting coefficient…
Autonomous multi-agent systems based on large language models (LLMs) have demonstrated remarkable abilities in independently solving complex tasks in a wide breadth of application domains. However, these systems hit critical reasoning,…
Tensor parallelism is an essential technique for distributed training of large neural networks. However, automatically determining an optimal tensor parallel strategy is challenging due to the gigantic search space, which grows…
We present a method to linearize, without approximation, a specific class of eigenvalue problems with eigenvector nonlinearities (NEPv), where the nonlinearities are expressed by scalar functions that are defined by a quotient of linear…
Many problems in machine learning and other fields can be (re)for-mulated as linearly constrained separable convex programs. In most of the cases, there are multiple blocks of variables. However, the traditional alternating direction method…
This paper presents the results of a preliminary experimental investigation of the performance of a stationary iterative method based on a block staircase splitting for solving singular systems of linear equations arising in Markov chain…
In this paper we consider the problem of computing generalized eigenvectors of a matrix pencil in real Schur form. In exact arithmetic, this problem can be solved using substitution. In practice, substitution is vulnerable to floating-point…
We describe a parallel solver for the discretized weakly singular space-time boundary integral equation of the spatially two-dimensional heat equation. The global space-time nature of the system matrices leads to improved parallel…
This paper is concerned with the development and analysis of an iterative solver for high-dimensional second-order elliptic problems based on subspace-based low-rank tensor formats. Both the subspaces giving rise to low-rank approximations…
Traditionally, there are several polynomial algorithms for linear programming including the ellipsoid method, the interior point method and other variants. Recently, Chubanov [Chubanov, 2015] proposed a projection and rescaling algorithm,…
Processors with large numbers of cores are becoming commonplace. In order to take advantage of the available resources in these systems, the programming paradigm has to move towards increased parallelism. However, increasing the level of…