Related papers: Accelerating Polynomial Homotopy Continuation on a…
Numerical integration of stochastic differential equations is commonly used in many branches of science. In this paper we present how to accelerate this kind of numerical calculations with popular NVIDIA Graphics Processing Units using the…
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"…
The vision of super computer at every desk can be realized by powerful and highly parallel CPUs or GPUs or APUs. Graphics processors once specialized for the graphics applications only, are now used for the highly computational intensive…
In this article, we develop and analyze a homotopy continuation method, referred to as HONES , for solving the sequential generalized projections in Online Newton Step, as well as the generalized problem known as sequential standard…
We combine tools from homotopy continuation solvers with the methods of analytic combinatorics in several variables to give the first practical algorithm and implementation for the asymptotics of multivariate rational generating functions…
The increasing scale and wealth of inter-connected data, such as those accrued by social network applications, demand the design of new techniques and platforms to efficiently derive actionable knowledge from large-scale graphs. However,…
Evolution can be broadly described in terms of mutations of the genotype and the subsequent selection of the phenotype. The full enumeration of a given genotype-phenotype (GP) map is therefore a powerful technique in examining evolutionary…
Time-domain radio astronomy utilizes a harmonic sum algorithm as part of the Fourier domain periodicity search, this type of search is used to discover single pulsars. The harmonic sum algorithm is also used as part of the Fourier domain…
The paper considers the problem of implementation on graphics processors of numerical integration routines for higher order finite element approximations. The design of suitable GPU kernels is investigated in the context of general purpose…
A theory of numerical path-following in toric varieties was suggested in two previous papers. The motivation is solving systems of polynomials with real or complex coefficients. When those polynomials are not assumed 'dense', solving them…
Large-scale linear programs (LPs) arise in many decision systems, including ranking, allocation, and matching problems that must be solved repeatedly at massive scale. Prior work such as ECLIPSE and LinkedIn's open-source DuaLip showed that…
With the advent of era of Big Data and Internet of Things, there has been an exponential increase in the availability of large data sets. These data sets require in-depth analysis that provides intelligence for improvements in methods for…
This research proposes a practical method for detecting featureless objects by using image alignment approach with a robust similarity measure in industrial applications. This similarity measure is robust against occlusion, illumination…
We study the computational complexity of a diagonalization technique for multivariate homogeneous polynomials, that is, expressing them as sums of powers of independent linear forms. It is based on Harrison's center theory and consists of a…
In this paper, we present an adaptive step-size homotopy tracking method for computing bifurcation points of nonlinear systems. There are four components in this new method: 1) an adaptive tracking technique is developed near bifurcation…
Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…
An arithmetic progression is a sequence of integers in which the difference between any two consecutive elements is the same. We investigate the parameterized complexity of two problems related to arithmetic progressions, called Cover by…
Inspired by numerical homotopy methods we propose a combinatorial homotopy algorithm for finding all isolated solutions to a tropical polynomial systems of n tropical polynomials in n variables. In particular, a tropicalisation of the…
The problem of verifying multi-threaded execution against the memory consistency model of a processor is known to be an NP hard problem. However polynomial time algorithms exist that detect almost all failures in such execution. These are…
Graphics Processing Units (GPUs) can speed up the numerical solution of various problems in astrophysics including the dynamical evolution of stellar systems; the performance gain can be more than a factor 100 compared to using a Central…