Related papers: Accelerating Polynomial Homotopy Continuation on a…
We develop a new method that improves the efficiency of equation-by-equation algorithms for solving polynomial systems. Our method is based on a novel geometric construction, and reduces the total number of homotopy paths that must be…
We develop a method for multidimensional optimisation using flow equations. This method is based on homotopy continuation in combination with a maximum entropy approach. Extrema of the optimising functional correspond to fixed points of the…
The realization space of geometric constraint systems is given by the vanishing locus of polynomials corresponding to natural geometric constraints. Such geometric constraint systems arise in many real-world scenarios such as structural…
Multipoint polynomial evaluation and interpolation are fundamental for modern symbolic and numerical computing. The known algorithms solve both problems over any field of constants in nearly linear arithmetic time, but the cost grows to…
The graphics processing unit (GPU) has emerged as a powerful and cost effective processor for general performance computing. GPUs are capable of an order of magnitude more floating-point operations per second as compared to modern central…
We consider the numerical irreducible decomposition of a positive dimensional solution set of a polynomial system into irreducible factors. Path tracking techniques computing loops around singularities connect points on the same irreducible…
Accurately predicting phonon scattering is crucial for understanding thermal transport properties. However, the computational cost of such calculations, especially for four-phonon scattering, can often be more prohibitive when large number…
As an important application of spatial databases in pathology imaging analysis, cross-comparing the spatial boundaries of a huge amount of segmented micro-anatomic objects demands extremely data- and compute-intensive operations, requiring…
Astronomers have come to rely on the increasing performance of computers to reduce, analyze, simulate and visualize their data. In this environment, faster computation can mean more science outcomes or the opening up of new parameter spaces…
We describe the use of Graphics Processing Units (GPUs) for speeding up the code NBODY6 which is widely used for direct $N$-body simulations. Over the years, the $N^2$ nature of the direct force calculation has proved a barrier for…
Modern real-time business analytic consist of heterogeneous workloads (e.g, database queries, graph processing, and machine learning). These analytic applications need programming environments that can capture all aspects of the constituent…
A polynomial homotopy is a family of polynomial systems in one parameter, which defines solution paths starting from known solutions and ending at solutions of a system that has to be solved. We consider paths leading to isolated singular…
Genetic Programming (GP) is a computationally intensive technique which also has a high degree of natural parallelism. Parallel computing architectures have become commonplace especially with regards Graphics Processing Units (GPU). Hence,…
Mathematical modelling allows us to concisely describe fundamental principles in biology. Analysis of models can help to both explain known phenomena, and predict the existence of new, unseen behaviours. Model analysis is often a complex…
Strong gravitational lensing is a powerful probe of cosmology and the dark matter distribution. Efficient lensing software is already a necessity to fully use its potential and the performance demands will only increase with the upcoming…
The Quadratic Assignment Problem (QAP) is an important combinatorial optimization problem with applications in many areas including logistics and manufacturing. QAP is known to be NP-hard, a computationally challenging problem, which…
Three-dimensional neutron transport calculations using the Method of Characteristics (MOC) are highly regarded for their exceptional computational efficiency, precision, and stability. Nevertheless, when dealing with extensive-scale…
Generation of optimal codes is a well known problem in coding theory. Many computational approaches exist in the literature for finding record breaking codes. However generating codes with long lengths $n$ using serial algorithms is…
The Macaulay2 package PHCpack.m2 provides an interface to PHCpack, a general-purpose polynomial system solver that uses homotopy continuation. The main method is a numerical blackbox solver which is implemented for all Laurent systems. The…
With the growing complexity and capability of contemporary robotic systems, the necessity of sophisticated computing solutions to efficiently handle tasks such as real-time processing, sensor integration, decision-making, and control…