相关论文: Extrapolating Solution Paths of Polynomial Homotop…
Numerical algebraic geometry provides a number of efficient tools for approximating the solutions of polynomial systems. One such tool is the parameter homotopy, which can be an extremely efficient method to solve numerous polynomial…
As we reach exascale, production High Performance Computing (HPC) systems are increasing in complexity. These systems now comprise multiple heterogeneous computing components (CPUs and GPUs) utilized through diverse, often vendor-specific…
An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…
The stationary points (SPs) of a potential energy landscape play a crucial role in understanding many of the physical or chemical properties of a given system. Unless they are found analytically, there is, however, no efficient method to…
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…
Molecular computing promises massive parallelization to explore solution spaces, but so far practical implementations remain limited due to off-target binding and exponential proliferation of competing structures. Here, we investigate the…
POCP is a new Matlab package running jointly with GloptiPoly 3 and, optionally, YALMIP. It is aimed at nonlinear optimal control problems for which all the problem data are polynomial, and provides an approximation of the optimal value as…
In this article, we introduce a new homotopy function to trace the trajectory by applying modified homotopy continuation method for finding the solution of the linear complementarity problem. Earlier several authors attempted to propose…
We introduce and study the complexity of Path Packing. Given a graph $G$ and a list of paths, the task is to embed the paths edge-disjoint in $G$. This generalizes the well known Hamiltonian-Path problem. Since Hamiltonian Path is…
We present a PDE-based approach for the multidimensional extrapolation of smooth scalar quantities across interfaces with kinks and regions of high curvature. Unlike the commonly used method of [2] in which normal derivatives are…
POLEVAL provides a software toolbox for collaborative, persistent and reproducible analysis of XPS experiments. It allows to treat, analyse and visualise the results of an extended experimental campaign in a single python notebook in a…
Phase retrieval deals with the estimation of complex-valued signals solely from the magnitudes of linear measurements. While there has been a recent explosion in the development of phase retrieval algorithms, the lack of a common interface…
We present a new continuation algorithm to find all nondegenerate real solutions to a system of polynomial equations. Unlike homotopy methods, it is not based on a deformation of the system; instead, it traces real curves connecting the…
The Promise Constraint Satisfaction Problem (PCSP for short) is a generalization of the well-studied Constraint Satisfaction Problem (CSP). The PCSP has its roots in such classic problems as the Approximate Graph Coloring and the…
This paper studies path synthesis for nonholonomic mobile robots moving in two-dimensional space. We first address the problem of interpolating paths expressed as sequences of straight line segments, such as those produced by some planning…
We describe, study, and experiment with an algorithm for finding all solutions of systems of polynomial equations using homotopy continuation and monodromy. This algorithm follows a framework developed in previous work and can operate in…
This paper presents a simplified implementation of the arc-length method for computing the equilibrium paths of nonlinear structural mechanics problems using the finite element method. In the proposed technique, the predictor is computed by…
For several computational problems in homotopy theory, we obtain algorithms with running time polynomial in the input size. In particular, for every fixed k>1, there is a polynomial-time algorithm that, for a 1-connected topological space X…
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…
A numerical irreducible decomposition for a polynomial system provides representations for the irreducible factors of all positive dimensional solution sets of the system, separated from its isolated solutions. Homotopy continuation methods…