Related papers: The Gauss quadrature for general linear functional…
This paper considers the problem of reconstructing missing parts of functions based on their observed segments. It provides, for Gaussian processes and arbitrary bijective transformations thereof, theoretical expressions for the…
A collection of subroutines and examples of their uses, as well as the underlying numerical methods, are described for generating orthogonal polynomials relative to arbitrary weight functions. The object of these routines is to produce the…
We consider the problem of numerically computing a critical point of a functional $J\colon M\rightarrow R$ where $M$ is a Riemannian manifold. Due to local quadratic convergence a popular choice to solve this problem is the geometric Newton…
We provide a necessary and sufficient condition for existence of Gaussian cubature formulas. It consists of checking whether some overdetermined linear system has a solution and so complements Mysovskikh's theorem which requires computing…
The aim of this note is to present a self-contained proof of the fact that a function can be approximated using a linear combination of Gaussian coherent states, with a number of terms controlled in terms of the smoothness and of the decay…
A partial least squares regression is proposed for estimating the function-on-function regression model where a functional response and multiple functional predictors consist of random curves with quadratic and interaction effects. The…
Sparse linear regression, which entails finding a sparse solution to an underdetermined system of linear equations, can formally be expressed as an $l_0$-constrained least-squares problem. The Orthogonal Least-Squares (OLS) algorithm…
The Grassmann manifold of linear subspaces is important for the mathematical modelling of a multitude of applications, ranging from problems in machine learning, computer vision and image processing to low-rank matrix optimization problems,…
We present a systematic computational framework for generating positive quadrature rules in multiple dimensions on general geometries. A direct moment-matching formulation that enforces exact integration on polynomial subspaces yields…
On some specified convex supporting sets of spheres, we find a generalized longitude function whose level sets are totally geodesic. Given an arbitrary (weakly) harmonic map into spheres, the composition of the generalized longitude…
Optimization of convex functions subject to eigenvalue constraints is intriguing because of peculiar analytical properties of eigenvalues, and is of practical interest because of wide range of applications in fields such as structural…
We extend the definition of the Costas property to functions in the continuum, namely on intervals of the reals or the rationals, and argue that such functions can be used in the same applications as discrete Costas arrays. We construct…
The bilateral filter is a versatile non-linear filter that has found diverse applications in image processing, computer vision, computer graphics, and computational photography. A widely-used form of the filter is the Gaussian bilateral…
The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the…
This article is concerned with Gaussian process quadratures, which are numerical integration methods based on Gaussian process regression methods, and sigma-point methods, which are used in advanced non-linear Kalman filtering and smoothing…
In theory, the Lanczos algorithm generates an orthogonal basis of the corresponding Krylov subspace. However, in finite precision arithmetic, the orthogonality and linear independence of the computed Lanczos vectors is usually lost quickly.…
In this paper we develop an optimisation based approach to multivariate Chebyshev approximation on a finite grid. We consider two models: multivariate polynomial approximation and multivariate generalised rational approximation. In the…
Orthogonal Fractional Factorial Designs and in particular Orthogonal Arrays are frequently used in many fields of application, including medicine, engineering and agriculture. In this paper we present a methodology and an algorithm to find…
Gauss-Lobatto quadrature nodes and weights are optimal for closed summation-by-parts (SBP) formulations based on polynomial approximation spaces in the sense that for a prescribed function space they yield an SBP operator of minimal…
The partial correlation graphical LASSO (PCGLASSO) is a penalised likelihood method for Gaussian graphical models which provides scale invariant sparse estimation of the precision matrix and improves upon the popular graphical LASSO method.…