Related papers: Accelerating Polynomial Homotopy Continuation on a…
Homotopy methods have proven to be a powerful tool for understanding the multitude of solutions provided by the coupled-cluster polynomial equations. This endeavor has been pioneered by quantum chemists that have undertaken both elaborate…
We consider polynomial systems of Prony type, appearing in many areas of mathematics. Their robust numerical solution is considered to be difficult, especially in "near-colliding" situations. We consider a case when the structure of the…
We introduce the concept of homotopy iterators for performing polynomial homotopy continuation tasks in a memory efficient manner. The main idea is to push forward an iterator for the start solutions of a homotopy via the function which…
In this work, we present an extension of Gaussian process (GP) models with sophisticated parallelization and GPU acceleration. The parallelization scheme arises naturally from the modular computational structure w.r.t. datapoints in the…
The conservative Post-Newtonian (PN) Hamiltonian formulation of spinning compact binaries has six integrals of motion including the total energy, the total angular momentum and the constant unit lengths of spins. The manifold correction…
In latest years, several advancements have been made in symbolic-numerical eigenvalue techniques for solving polynomial systems. In this article, we add to this list. We design an algorithm which solves systems with isolated solutions…
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…
We describe, for the first time, a completely rigorous homotopy (path--following) algorithm (in the Turing machine model) to find approximate zeros of systems of polynomial equations. If the coordinates of the input systems and the initial…
The goal of this paper is to study the path-following method for univariate polynomials. We propose to study the complexity and condition properties when the Newton method is applied as a correction operator. Then we study the geodesics and…
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 provide a preliminary study on utilizing GPU (Graphics Processing Unit) to accelerate computation for three simulation optimization tasks with either first-order or second-order algorithms. Compared to the implementation using only CPU…
Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation, and model selection. These are all optimization problems, well-known to be challenging due to…
- In this paper we introduce a new method to solve fixed-delay optimal control problems which exploits numerical homotopy procedures. It is known that solving this kind of problems via indirect methods is complex and computationally…
We present the Julia package SagbiHomotopy.jl for solving systems of polynomial equations using numerical homotopy continuation. The package introduces an optimal choice of a start system based on SAGBI homotopies. For square horizontally…
Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms, e.g., based on gradient descent or conjugate gradient methods that are at the core of control, machine…
The solutions of a system of polynomials in several variables are often needed, e.g.: in the design of mechanical systems, and in phase-space analyses of nonlinear biological dynamics. Reliable, accurate, and comprehensive numerical…
The alternating direction method of multipliers (ADMM) is a powerful operator splitting technique for solving structured convex optimization problems. Due to its relatively low per-iteration computational cost and ability to exploit…
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…
Cryptographic schemes like Fully Homomorphic Encryption (FHE) and Zero-Knowledge Proofs (ZKPs), while offering powerful privacy-preserving capabilities, are often hindered by their computational complexity. Polynomial multiplication, a core…
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…