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The Kernel Polynomial Method (KPM) is one of the fast diagonalization methods used for simulations of quantum systems in research fields of condensed matter physics and chemistry. The algorithm has a difficulty to be parallelized on a…
Clawpack is a library for solving nonlinear hyperbolic partial differential equations using high-resolution finite volume methods based on Riemann solvers and limiters. It supports Adaptive Mesh Refinement (AMR), which is essential in…
Krylov subspace methods are a powerful tool for efficiently solving high-dimensional linear algebra problems. In this work, we study the approximation quality that a Krylov subspace provides for estimating the numerical range of a matrix.…
Matrix multiplication is a foundational operation in scientific computing and machine learning, yet its computational complexity makes it a significant bottleneck for large-scale applications. The shift to parallel architectures, primarily…
This paper introduces a new class of algorithms for solving large-scale linear inverse problems based on new flexible and inexact Golub-Kahan factorizations. The proposed methods iteratively compute regularized solutions by approximating a…
In this work, we optimize speculative sampling for parallel hardware accelerators to improve sampling speed. We notice that substantial portions of the intermediate matrices necessary for speculative sampling can be computed concurrently.…
The solution of sparse symmetric positive definite linear systems is an important computational kernel in large-scale scientific and engineering modeling and simulation. We will solve the linear systems using a direct method, in which a…
We present a class of algorithms based on rational Krylov methods to compute the action of a generalized matrix function on a vector. These algorithms incorporate existing methods based on the Golub-Kahan bidiagonalization as a special…
In this paper we present deflation and augmentation techniques that have been designed to accelerate the convergence of Krylov subspace methods for the solution of linear systems of equations. We review numerical approaches both for linear…
Although the performance of commodity computers has improved drastically with the introduction of multicore processors and GPU computing, the standard R distribution is still based on single-threaded model of computation, using only a small…
Finite element schemes based on discontinuous Galerkin methods possess features amenable to massively parallel computing accelerated with general purpose graphics processing units (GPUs). However, the computational performance of such…
Graphical processing units (GPUs) promise to revolutionize scientific computing in the near future. Already, they allow almost real-time integration of simplified numerical models of cardiac tissue dynamics. However, the integration methods…
We describe the GPU implementation of shifted or multimass iterative solvers for sparse linear systems of the sort encountered in lattice gauge theory. We provide a generic tool that can be used by those without GPU programming experience…
Tikhonov regularization is a widely used technique in solving inverse problems that can enforce prior properties on the desired solution. In this paper, we propose a Krylov subspace based iterative method for solving linear inverse problems…
Most current prevalent iterative methods can be classified into the so-called extended Krylov subspace methods, a class of iterative methods which do not fall into this category are also proposed in this paper. Comparing with traditional…
Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…
We present a highly parallel implementation of the cross-correlation of time-series data using graphics processing units (GPUs), which is scalable to hundreds of independent inputs and suitable for the processing of signals from "Large-N"…
Ising Machines are emerging hardware architectures that efficiently solve NP-Hard combinatorial optimization problems. Generally, combinatorial problems are transformed into quadratic unconstrained binary optimization (QUBO) form, but this…
When an iterative method is applied to solve the linear equation system in interior point methods (IPMs), the attention is usually placed on accelerating their convergence by designing appropriate preconditioners, but the linear solver is…
We present and release in open source format a sparse linear solver which efficiently exploits heterogeneous parallel computers. The solver can be easily integrated into scientific applications that need to solve large and sparse linear…