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In order to compensate for the higher cost of double double and quad double arithmetic when solving large polynomial systems, we investigate the application of NVIDIA Tesla K20C general purpose graphics processing unit. The focus on this…
Our problem is to accurately solve linear systems on a general purpose graphics processing unit with double double and quad double arithmetic. The linear systems originate from the application of Newton's method on polynomial systems.…
The problem is to evaluate a polynomial in several variables and its gradient at a power series truncated to some finite degree with multiple double precision arithmetic. To compensate for the cost overhead of multiple double precision and…
The paper presents the aspect of use of modern graphics accelerators supporting CUDA technology for high-performance computing in the field of linear algebra. Fully programmable graphic cards have been available for several years for both…
We present an optimized algorithm calculating determinant for multivariate polynomial matrix on GPU. The novel algorithm provides precise determinant for input multivariate polynomial matrix in controllable time. Our approach is based on…
Numerical continuation methods track a solution path defined by a homotopy. The systems we consider are defined by polynomials in several variables with complex coefficients. For larger dimensions and degrees, the numerical conditioning…
Polynomial systems occur in many areas of science and engineering. Unlike general nonlinear systems, the algebraic structure enables to compute all solutions of a polynomial system. We describe our massive parallel predictor-corrector…
The clustering coefficient and the transitivity ratio are concepts often used in network analysis, which creates a need for fast practical algorithms for counting triangles in large graphs. Previous research in this area focused on…
A polynomial homotopy is a family of polynomial systems, typically in one parameter $t$. Our problem is to compute power series expansions of the coordinates of the solutions in the parameter $t$, accurately, using multiple double…
The main objective of this work consists in analyzing sub-structuring method for the parallel solution of sparse linear systems with matrices arising from the discretization of partial differential equations such as finite element, finite…
We present a new adaptive parallel algorithm for the challenging problem of multi-dimensional numerical integration on massively parallel architectures. Adaptive algorithms have demonstrated the best performance, but efficient many-core…
Hardware accelerators (such as Nvidia's CUDA GPUs) have tremendous promise for computational science, because they can deliver large gains in performance at relatively low cost. In this work, we focus on the use of Nvidia's Tesla GPU for…
The goal of this work is to parallelize the multistep scheme for the numerical approximation of the backward stochastic differential equations (BSDEs) in order to achieve both, a high accuracy and a reduction of the computation time as…
The problem of solving a system of polynomial equations is one of the most fundamental problems in applied mathematics. Among them, the problem of solving a system of binomial equations form a important subclass for which specialized…
Hardware double precision is often insufficient to solve large scientific problems accurately. Computing in higher precision defined by software causes significant computational overhead. The application of parallel algorithms compensates…
Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solution of discrete variational equations for boundary value…
We examine the problem of optimizing classification tree evaluation for on-line and real-time applications by using GPUs. Looking at trees with continuous attributes often used in image segmentation, we first put the existing algorithms for…
We consider differential Lyapunov and Riccati equations, and generalized versions thereof. Such equations arise in many different areas and are especially important within the field of optimal control. In order to approximate their…
We demonstrate a high-performance vendor-agnostic method for massively parallel solving of ensembles of ordinary differential equations (ODEs) and stochastic differential equations (SDEs) on GPUs. The method is integrated with a widely used…
Selected inversion is essential for applications such as Bayesian inference, electronic structure calculations, and inverse covariance estimation, where computing only specific elements of large sparse matrix inverses significantly reduces…