Related papers: Efficiently transforming from values of a function…

An efficient procedure for the computation of the coefficients of Legendre expansions is here presented. We prove that the Legendre coefficients associated with a function f(x) can be represented as the Fourier coefficients of an Abel-type…

Spatial functional data arise in many settings, such as particulate matter curves observed at monitoring stations and age population curves at each areal unit. Most existing functional regression models have limited applicability because…

The main aim of this paper is to provide a novel approach to deriving identities for the Bernstein polynomials using functional equations. We derive various functional equations and differential equations using generating functions.…

We propose a novel, efficient approach for distributed sparse learning in high-dimensions, where observations are randomly partitioned across machines. Computationally, at each round our method only requires the master machine to solve a…

Our main interest in this paper is to study some approximation problems for classes of functions with mixed smoothness. We use technique, based on a combination of results from hyperbolic cross approximation, which were obtained in 1980s --…

This paper is concerned with developing an efficient numerical algorithm for fast implementation of the sparse grid method for computing the $d$-dimensional integral of a given function. The new algorithm, called the MDI-SG ({\em multilevel…

Covariance function estimation is a fundamental task in multivariate functional data analysis and arises in many applications. In this paper, we consider estimating sparse covariance functions for high-dimensional functional data, where the…

Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered datasets in d-dimensional space. It is non-separable approximation, as it is…

In a previous paper [1] it was discussed the viability of functional analysis using as a basis a couple of generic functions, and hence vectorial decomposition. Here we complete the paradigm exploiting one of the analysis methodologies…

In geostatistics, traditional spatial models often rely on the Gaussian Process (GP) to fit stationary covariances to data. It is well known that this approach becomes computationally infeasible when dealing with large data volumes,…

Approximation of scattered geometric data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This method is useful for…

Recently isotropic basis functions of $N$ unit vector arguments were presented; these are of significant use in measuring the N-Point Correlation Functions (NPCFs) of galaxy clustering. Here we develop the generating function for these…

A general approach was proposed in this article to develop high-order exponentially fitted basis functions for finite element approximations of multi-dimensional drift-diffusion equations for modeling biomolecular electrodiffusion…

Gradient matching is a promising tool for learning parameters and state dynamics of ordinary differential equations. It is a grid free inference approach, which, for fully observable systems is at times competitive with numerical…

This paper proposes and analyzes fully data driven methods for inference about the mean function of a stochastic process from a sample of independent trajectories of the process, observed at discrete time points and corrupted by additive…

We develop an algorithm that combines model-based and model-free methods for solving a nonlinear optimal control problem with a quadratic cost in which the system model is given by a linear state-space model with a small additive nonlinear…

In the design flow of integrated circuits, chip-level verification is an important step that sanity checks the performance is as expected. Power grid verification is one of the most expensive and time-consuming steps of chip-level…

A dimension reduction method based on the "Nonlinear Level set Learning" (NLL) approach is presented for the pointwise prediction of functions which have been sparsely sampled. Leveraging geometric information provided by the Implicit…

In a number of situations, collecting a function value for every data point may be prohibitively expensive, and random sampling ignores any structure in the underlying data. We introduce a scalable optimization algorithm with no correction…

We address the problem of constructing varying-coefficient models based on basis expansions along with the technique of regularization. A crucial point in our modeling procedure is the selection of smoothing parameters in the regularization…