Related papers: The Pad\'e matrix pencil method with spurious pole…
In this paper, we consider the particular case of the general rational Hermite interpolation problem where only the value of the function is interpolated at some points, and where the function and its first derivatives agree at the origin.…
The nonlinear inverse problem of exponential data fitting is separable since the fitting function is a linear combination of parameterized exponential functions, thus allowing to solve for the linear coefficients separately from the…
We investigate the rational approximation of fractional powers of unbounded positive operators attainable with a specific integral representation of the operator function. We provide accurate error bounds by exploiting classical results in…
In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent…
In this article, we construct new Pad\'{e} approximations for the \emph{product} of binomial functions and powers of logarithmic functions. While several explicit Pad\'{e} approximants are known for powers of exponential functions, binomial…
Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…
This work presents a new algorithm to compute the matrix exponential within a given tolerance. Combined with the scaling and squaring procedure, the algorithm incorporates Taylor, partitioned and classical Pad\'e methods shown to be…
In the context of the anomalous magnetic moment of the muon, the hadronic contribution plays a crucial role, especially given its large contribution to the final error. Currently, lattice QCD simulations are in disagreement with dispersive…
We introduce a new method for estimating determinants or determinant ratios of large matrices, which combines the techniques of Pad\`{e} approximation with rational functions and $Z_{2}$ noise estimation of traces of large matrices. The…
This paper establishes an approximation theorem for randomized neural networks (RaNNs) whose hidden-layer parameters are uniformly sampled from a prescribed bounded domain. Our analysis shows that, for RaNNs of the form $\mathop{\sum}_i W_i…
A novel matrix approximation problem is considered herein: observations based on a few fully sampled columns and quasi-polynomial structural side information are exploited. The framework is motivated by quantum chemistry problems wherein…
We propose a method based on minimum-variance polynomial approximation to extract system poles from a data set of samples of the impulse response of a linear system. The method is capable of handling the problem under general conditions of…
MAP is the problem of finding a most probable instantiation of a set of variables given evidence. MAP has always been perceived to be significantly harder than the related problems of computing the probability of a variable instantiation…
We present a new rational approximation algorithm based on the empirical interpolation method for interpolating a family of parametrized functions to rational polynomials with invariant poles, leading to efficient numerical algorithms for…
Recently we developed a new sampling methodology based on incomplete cosine expansion of the sinc function and applied it in numerical integration in order to obtain a rational approximation for the complex error function $w\left(z \right)…
We consider the related tasks of matrix completion and matrix approximation from missing data and propose adaptive sampling procedures for both problems. We show that adaptive sampling allows one to eliminate standard incoherence…
Probabilistic circuits (PCs) such as sum-product networks efficiently represent large multi-variate probability distributions. They are preferred in practice over other probabilistic representations such as Bayesian and Markov networks…
The main purpose of the paper is to present some powerful data on the advantage of the rational approximation procedure based on Hermite-Pad\'e polynomials over the Pad\'e approximation procedure. The first part of the paper is devoted to…
Generally, discretization of partial differential equations (PDEs) creates a sequence of linear systems $A_k x_k = b_k, k = 0, 1, 2, ..., N$ with well-known and structured sparsity patterns. Preconditioners are often necessary to achieve…
A two-step method for solving planar Laplace problems via rational approximation is introduced. First complex rational approximations to the boundary data are determined by AAA approximation, either globally or locally near each corner or…