Related papers: The Pad\'e matrix pencil method with spurious pole…
The problem of having to reconstruct the decay rates and corresponding amplitudes of the single-exponential components of a noisy multi-exponential signal is common in many other areas of physics and engineering besides lattice field…
In paper a new definition of reduced Pade approximant and algorithm for its computing is proposed. Our approach is based on the investigation of the kernel structure of the Toeplitz matrix. It is shown that the reduced Pade approximant…
We consider the problem of computing univariate polynomial matrices over a field that represent minimal solution bases for a general interpolation problem, some forms of which are the vector M-Pad\'e approximation problem in [Van Barel and…
Probabilistic circuits (PCs) are a class of tractable probabilistic models that allow efficient, often linear-time, inference of queries such as marginals and most probable explanations (MPE). However, marginal MAP, which is central to many…
MAP is the problem of finding a most probable instantiation of a set of variables in a Bayesian network given some evidence. Unlike computing posterior probabilities, or MPE (a special case of MAP), the time and space complexity of…
Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as l1-norm and l2, p-norm, can deal with noise or outliers to some…
Given a redundant dictionary $\Phi$, represented by an $M \times N$ matrix ($\Phi \in \mathbb{R}^{M \times N}$) and a target signal $y \in \mathbb{R}^M$, the \emph{sparse approximation problem} asks to find an approximate representation of…
We introduce a new method for Estimation of Signal Parameters based on Iterative Rational Approximation (ESPIRA) for sparse exponential sums. Our algorithm uses the AAA algorithm for rational approximation of the discrete Fourier transform…
This paper focuses on numerical approximation for fractional powers of elliptic operators on $2$-d manifolds. Firstly, parametric finite element method is employed to discretize the original problem. We then approximate fractional powers of…
We introduce a simple, rigorous, and unified framework for solving nonlinear partial differential equations (PDEs), and for solving inverse problems (IPs) involving the identification of parameters in PDEs, using the framework of Gaussian…
Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…
Pad\'e approximants are rational functions whose series expansion match a given series as far as possible. These approximants are usually written under a rational form. In this paper, we will show how to write them also under two different…
Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply…
Planar markers are useful in robotics and computer vision for mapping and localisation. Given a detected marker in an image, a frequent task is to estimate the 6DOF pose of the marker relative to the camera, which is an instance of planar…
A new scaling and recovering algorithm is proposed for simultaneously computing the matrix $\varphi$-functions that arise in exponential integrator methods for the numerical solution of certain first-order systems of ordinary differential…
We investigate the Pad\'e approximation method for the analytic continuation of numerical data and its ability to access, from the Euclidean propagator, both the spectral function and part of the physical information hidden in the second…
In this article we obtain new irrationality measures for values of functions which belong to a certain class of hypergeometric functions including shifted logarithmic functions, binomial functions and shifted exponential functions. We…
We introduce a novel algorithm that computes the $k$-sparse principal component of a positive semidefinite matrix $A$. Our algorithm is combinatorial and operates by examining a discrete set of special vectors lying in a low-dimensional…
Motivated by a use case in theoretical hadron physics, we revisit an application of a pole-sum fit to dressing functions of a confined quark propagator. More precisely, we investigate approaches to determine the number and positions of the…
This paper studies the numerical approximation of parametric time-dependent partial differential equations (PDEs) by proper orthogonal decomposition reduced order models (POD-ROMs). Although many papers in the literature consider reduced…