Related papers: Complexity of Path-Following Methods for the Eigen…
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…
We introduce a new complexity measure of a path of (problems, solutions) pairs in terms of the length of the path in the condition metric which we define in the article. The measure gives an upper bound for the number of Newton steps…
Parametric path problems arise independently in diverse domains, ranging from transportation to finance, where they are studied under various assumptions. We formulate a general path problem with relaxed assumptions, and describe how this…
We propose a new proximal, path-following framework for a class of constrained convex problems. We consider settings where the nonlinear---and possibly non-smooth---objective part is endowed with a proximity operator, and the constraint set…
Finding paths in graphs is a fundamental graph-theoretic task. In this work, we we are concerned with finding a path with some constraints on its length and the number of vertices neighboring the path, that is, being outside of and incident…
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…
In two and three dimensions, we analyze a finite element method to approximate the solutions of an eigenvalue problem arising from neutron transport. We derive the eigenvalue problem of interest, which results to be non-symmetric. Under a…
We study a probabilistic variant of the r-th sequential parametrized topological complexity, which bounds this classical invariant from below and measures the difficulty in constructing permissive parametrized motion planning algorithms. On…
We present a new approach to compute eigenvalues and eigenvectors of locally definite multiparameter eigenvalue problems by its signed multiindex. The method has the interpretation of a semismooth Newton method applied to certain functions…
The embedding problem is to decide, given an ordered pair of structures, whether or not there is an injective homomorphism from the first structure to the second. We study this problem using an established perspective in parameterized…
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…
A lower bound on the solution to the traveling salesman problem is provided, which is expressed in terms of eigenvalues related to the distance matrix for the problem. This bound has many interesting properties such as transforming…
In many high-frequency simulation workflows, eigenvalue tracking along a parameter variation is necessary. This can become computationally prohibitive when repeated time-consuming eigenvalue problems must be solved. Therefore, we employ a…
In this work, we show that the eigenvalue continuation approach introduced recently in [Phys. Rev. Lett. {\bf 121}, 032501 (2018)], despite its many advantages, has some fundamental limitations which cannot be overcome when strongly…
A novel method for approximating structured singular values (also known as mu-values) is proposed and investigated. These quantities constitute an important tool in the stability analysis of uncertain linear control systems as well as in…
The paper focuses on the problem of tracking eigenvalue trajectories in large-scale power system models as system parameters vary. A continuation-based formulation is presented for tracing any single eigenvalue of interest, which supports…
We discuss an eigenvalue problem which arises in the studies of asymptotic stability of a self-similar attractor in the sigma model. This problem is rather unusual from the viewpoint of the spectral theory of linear operators and requires…
This article considers the problem of solving a system of $n$ real polynomial equations in $n+1$ variables. We propose an algorithm based on Newton's method and subdivision for this problem. Our algorithm is intended only for nondegenerate…
We study the complexity of invariant inference and its connections to exact concept learning. We define a condition on invariants and their geometry, called the fence condition, which permits applying theoretical results from exact concept…
Given a square complex matrix $A$, we tackle the problem of finding the nearest matrix with multiple eigenvalues or, equivalently when $A$ had distinct eigenvalues, the nearest defective matrix. To this goal, we extend the general framework…