Related papers: Pole-fitting for complex functions: enhancing stan…
Quadratic programming is a workhorse of modern nonlinear optimization, control, and data science. Although regularized methods offer convergence guarantees under minimal assumptions on the problem data, they can exhibit the slow…
In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…
We extend the standard notion of self-concordance to non-convex optimization and develop a family of second-order algorithms with global convergence guarantees. In particular, two function classes -- \textit{weakly self-concordant}…
Tensor network contractions are widely used in statistical physics, quantum computing, and computer science. We introduce a method to efficiently approximate tensor network contractions using low-rank approximations, where each intermediate…
We study AAK-type meromorphic approximants to functions $F$, where $F$ is a sum of a rational function $R$ and a Cauchy transform of a complex measure $\lambda$ with compact regular support included in $(-1,1)$, whose argument has bounded…
Sparse grids based on Lagrange polynomials have become one of the staple methods for approximating functions that are high-dimensional and expensive to evaluate, in the context e.g. of PDE-based parametric design exploration. They are…
Ensembling methods are well known for improving prediction accuracy. However, they are limited in the sense that they cannot discriminate among component models effectively. In this paper, we propose stacking with auxiliary features that…
We present two algorithms for constructing orthonormal bases of rational function vectors with respect to a discrete inner product, and discuss how to use them for a rational approximation problem. Building on the pencil-based formulation…
Results are presented for the numerical verification of a method devised to identify an unknown spatio-temporal distribution of heat flux that occurs at the surface of thin aluminum plate, as a result of pulsed, high-power laser beam…
We present fully polynomial approximation schemes for a broad class of Holant problems with complex edge weights, which we call Holant polynomials. We transform these problems into partition functions of abstract combinatorial structures…
Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in…
We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…
We analyze the problem of global reconstruction of functions as accurately as possible, based on partial information in the form of a truncated power series at some point, and additional analyticity properties. This situation occurs…
The pole assignment problem for descriptor systems is a classical inverse algebraic eigenvalue problem, which has attracted attention for decades. In this paper, we propose a direct method to solve the problem with the application of the…
We present an algorithm to estimate the rotation pole of a principal-axis rotator using silhouette images collected from multiple camera poses. First, a set of images is stacked to form a single silhouette-stack image, where the object's…
Large-scale optimization problems arising from the discretization of problems involving PDEs sometimes admit solutions that can be well approximated by low-rank matrices. In this paper, we will exploit this low-rank approximation property…
We develop improved rearrangement algorithms to find the dependence structure that minimizes a convex function of the sum of dependent variables with given margins. We propose a new multivariate dependence measure, which can assess the…
Pole-swapping algorithms, generalizations of bulge-chasing algorithms, have been shown to be a viable alternative to the bulge-chasing QZ algorithm for solving the generalized eigenvalue problem for a matrix pencil A - {\lambda}B. It is…
For systems of unstable particles that mix with each other, an approximation of the fully momentum-dependent propagator matrix is presented in terms of a sum of simple Breit-Wigner propagators that are multiplied with finite on-shell wave…
We show that under some widely believed assumptions, there are no higher-order algorithms for basic tasks in computational mathematics such as: Computing integrals with neural network integrands, computing solutions of a Poisson equation…