Related papers: GPU-Based Homotopy Continuation for Minimal Proble…
While automatically generated polynomial elimination templates have sparked great progress in the field of 3D computer vision, there remain many problems for which the degree of the constraints or the number of unknowns leads to…
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…
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…
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 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…
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…
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 manuscript addresses the problem of finding all solutions of power flow equations or other similar nonlinear system of algebraic equations. This problem arises naturally in a number of power systems contexts, most importantly in the…
A special homotopy continuation method, as a combination of the polyhedral homotopy and the linear product homotopy, is proposed for computing all the isolated solutions to a special class of polynomial systems. The root number bound of…
Polynomial systems occur in many fields of science and engineering. Polynomial homotopy continuation methods apply symbolic-numeric algorithms to solve polynomial systems. We describe the design and implementation of our web interface and…
We propose a high-performance GPU solver for inverse homogenization problems to design high-resolution 3D microstructures. Central to our solver is a favorable combination of data structures and algorithms, making full use of the parallel…
Convex optimization encompasses a wide range of optimization problems that contain many efficiently solvable subclasses. Interior point methods are currently the state-of-the-art approach for solving such problems, particularly effective…
Hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows to integrate higher-order geometric information. Hypergraph matching can be formulated as a third-order…
We design, implement, and evaluate GPU-based algorithms for the maximum cardinality matching problem in bipartite graphs. Such algorithms have a variety of applications in computer science, scientific computing, bioinformatics, and other…
The adoption of hybrid GPU-CPU nodes in traditional supercomputing platforms opens acceleration opportunities for electronic structure calculations in materials science and chemistry applications, where medium sized Hermitian generalized…
The study of models with extended Higgs sectors requires to minimize the corresponding Higgs potentials, which is in general very difficult. Here, we apply a recently developed method, called numerical polynomial homotopy continuation…
We propose a new hybrid topology optimization algorithm based on multigrid approach that combines the parallelization strategy of CPU using OpenMP and heavily multithreading capabilities of modern Graphics Processing Units (GPU). In…
Recent years have witnessed a rapid advancement in GPU technology, establishing it as a formidable high-performance parallel computing technology with superior floating-point computational capabilities compared to traditional CPUs. This…
We present a method for solving two minimal problems for relative camera pose estimation from three views, which are based on three view correspondences of i) three points and one line and the novel case of ii) three points and two lines…
Homomorphic Encryption (HE) enables users to securely outsource both the storage and computation of sensitive data to untrusted servers. Not only does HE offer an attractive solution for security in cloud systems, but lattice-based HE…