Related papers: Quality Up in Polynomial Homotopy Continuation by …
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…
We consider the problem of tracking one solution path defined by a polynomial homotopy on a parallel shared memory computer. Our robust path tracker applies Newton's method on power series to locate the closest singular parameter value. On…
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…
We propose a new algorithm for numerical path tracking in polynomial homotopy continuation. The algorithm is `robust' in the sense that it is designed to prevent path jumping and in many cases, it can be used in (only) double precision…
The polyhedral homotopy method of Huber and Sturmfels is a particularly efficient and robust numerical method for solving system of (Laurent) polynomial equations. A central component in an implementation of this method is an efficient and…
Three aspects of applying homotopy continuation, which is commonly used to solve parameterized systems of polynomial equations, are investigated. First, for parameterized systems which are homogeneous, we investigate options for performing…
Quantum coherence allows the computation of an arbitrary number of distinct computational paths in parallel. Based on quantum parallelism it has been conjectured that exponential or even larger speedups of computations are possible. Here it…
The constrained path optimization (CPO) problem takes the following input: (a) a road network represented as a directed graph, where each edge is associated with a "cost" and a "score" value; (b) a source-destination pair and; (c) a budget…
Heterogeneous multi-core systems such as big/little architectures have been introduced as an attractive server design option with the potential to improve performance under power constraints in data centres. Since both big high-performing…
In this paper, we present multi-threaded algorithms for graph coloring suitable to the shared memory programming model. We modify an existing algorithm widely used in the literature and prove the correctness of the modified algorithm. We…
This article presents an automatic approach to quickly derive a good solution for hardware resource partition and task granularity for task-based parallel applications on heterogeneous many-core architectures. Our approach employs a…
Evaluating how well a whole system or set of subsystems performs is one of the primary objectives of performance testing. We can tell via performance assessment if the architecture implementation meets the design objectives. Performance…
Systems of polynomial equations arise frequently in computer vision, especially in multiview geometry problems. Traditional methods for solving these systems typically aim to eliminate variables to reach a univariate polynomial, e.g., a…
Microprocessors have revolutionized the world we live in and continuous efforts are being made to manufacture not only faster chips but also smarter ones. A number of techniques such as data level parallelism, instruction level parallelism…
We discuss the advantages of parallelization by multithreading on graphics processing units (GPUs) for parallel tempering Monte Carlo computer simulations of an exemplified bead-spring model for homopolymers. Since the sampling of a large…
Heterogeneous multi core processors can offer diverse computing capabilities. The efficiency of Market Basket Analysis Algorithm can be improved with heterogeneous multi core processors. Market basket analysis algorithm utilises apriori…
Parallel computing is a standard approach to achieving high-performance computing (HPC). Three commonly used methods to implement parallel computing include: 1) applying multithreading technology on single-core or multi-core CPUs; 2)…
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…
We use our recent implementation of a certified homotopy tracking algorithm to search for start systems that minimize the average complexity of finding all roots of a regular system of polynomial equations. While finding optimal start…