Related papers: Accelerating Polynomial Homotopy Continuation on a…
In the present paper we show a dichotomy theorem for the complexity of polynomial evaluation. We associate to each graph H a polynomial that encodes all graphs of a fixed size homomorphic to H. We show that this family is computable by…
Process mapping asks to assign vertices of a task graph to processing elements of a supercomputer such that the computational workload is balanced while the communication cost is minimized. Motivated by the recent success of GPU-based graph…
We study a graph partitioning problem motivated by the simulation of the physical movement of multi-body systems on an atomistic level, where the forces are calculated from a quantum mechanical description of the electrons. Several advanced…
Persistent homology is a crucial invariant that is used in many areas to understand data. The $O(N^4)$ run time is a hindrance to its use on most large datasets. We give a parallelization method to utilize multi-core machines and clusters.…
Graphics Processing Unit (GPU) computing is becoming an alternate computing platform for numerical simulations. However, it is not clear which numerical scheme will provide the highest computational efficiency for different types of…
The edge computing paradigm has emerged to handle cloud computing issues such as scalability, security and low response time among others. This new computing trend heavily relies on ubiquitous embedded systems on the edge. Performance and…
Large-scale strongly nonlinear and nonconvex mixed-integer nonlinear programming (MINLP) models frequently appear in optimisation-based process synthesis, integration, intensification, and process control. However, they are usually…
The IEEE 754-2008 standard recommends the correct rounding of some elementary functions. This requires to solve the Table Maker's Dilemma which implies a huge amount of CPU computation time. We consider in this paper accelerating such…
Symmetry plays a central role in accelerating symbolic computation involving polynomials. This chapter surveys recent developments and foundational methods that leverage the inherent symmetries of polynomial systems to reduce complexity,…
We consider dynamical models given by rational ODE systems. Parameter estimation is an important and challenging task of recovering parameter values from observed data. Recently, a method based on differential algebra and rational…
This paper deals with linear algebra operations on Graphics Processing Unit (GPU) with complex number arithmetic using double precision. An analysis of their uses within iterative Krylov methods is presented to solve acoustic problems.…
We design a homotopy continuation algorithm, that is based on numerically tracking Viro's patchworking method, for finding real zeros of sparse polynomial systems. The algorithm is targeted for polynomial systems with coefficients…
This paper presents efforts to improve the hierarchical parallelism of a two scale simulation code. Two methods to improve the GPU parallel performance were developed and compared. The first used the NVIDIA Multi-Process Service and the…
In this paper, we propose a carefully optimized "half-gcd" algorithm for polynomials. We achieve a constant speed-up with respect to previous work for the asymptotic time complexity. We also discuss special optimizations that are possible…
In this paper we solve on GPUs massive problems with large amount of data, which are not appropriate for solution with the SIMD technology. For the given problem we consider a three-level parallelization. The multithreading of CPU is used…
We accelerated an ab-initio molecular QMC calculation by using GPGPU. Only the bottle-neck part of the calculation is replaced by CUDA subroutine and performed on GPU. The performance on a (single core CPU + GPU) is compared with that on a…
The ability to timely process significant amounts of continuously updated spatial data is mandatory for an increasing number of applications. Parallelism enables such applications to face this data-intensive challenge and allows the devised…
Pseudo-arclength continuation is a well-established method for generating a numerical curve approximating the solution of an underdetermined system of nonlinear equations. It is an inherently sequential predictor-corrector method in which…
Let $\K$ be a field of characteristic zero and $\Kbar$ be an algebraic closure of $\K$. Consider a sequence of polynomials$G=(g\_1,\dots,g\_s)$ in $\K[X\_1,\dots,X\_n]$, a polynomial matrix $\F=[f\_{i,j}] \in \K[X\_1,\dots,X\_n]^{p \times…
A path tracking algorithm that adaptively adjusts precision is presented. By adjusting the level of precision in accordance with the numerical conditioning of the path, the algorithm achieves high reliability with less computational cost…