Related papers: Multifractal Interpolation of Universal Multifract…
The present work proposes the concept of induced percolation over multiple-object systems, so that features such as the number of merged clusters can be used as a relevant measurement. The suggested approach involves the expansion of the…
Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary…
The multigrid algorithm is a multilevel approach to accelerate the numerical solution of discretized differential equations in physical problems involving long-range interactions. Multiresolution analysis of wavelet theory provides an…
We present a new technique for the interpolation of discretely-sampled non-negat ive scalar fields across regions of missing data. Any set of basis functions can be used, though the method is fastest when they are close to orthogonal. We…
Multiresolution analyses based upon interpolets, interpolating scaling functions introduced by Deslauriers and Dubuc, are particularly well-suited to physical applications because they allow exact recovery of the multiresolution…
Global and local regularities of functions are analyzed in anisotropic function spaces, under a common framework, that of hyperbolic wavelet bases. Local and directional regularity features are characterized by means of global quantities…
We consider interpolation of univariate functions on arbitrary sets of nodes by Gaussian radial basis functions or by exponential functions. We derive closed-form expressions for the interpolation error based on the…
Inverse problem or parameter estimation of ordinary differential equations (ODEs), the iterative process of minimizing the mismatch between model-predicted and experimental states by tuning the parameter values within an optimization…
In a series of papers (Lombardi & Schneider 2001, 2002) we studied in detail the statistical properties of an interpolation technique widely used in astronomy. In particular, we considered the average interpolated map and its covariance…
The properties of the compactness of interpolation sets of algebras of generalized analytic functions are investigated and convenient sufficient conditions for interpolation are given.
We study the sets of points where a L\'evy function and a translated L\'evy function share a given couple of H\''older exponents, and we investigate how their Hausdorff dimensions depend on the translation parameter.
This paper introduces the fractal interpolation problem defined over domains with a nonlinear partition. This setting generalizes known methodologies regarding fractal functions and provides a new holistic approach to fractal interpolation.…
When approximating a function that depends on a parameter, one encounters many practical examples where linear interpolation or linear approximation with respect to the parameters prove ineffective. This is particularly true for responses…
We characterize the region of meromorphic continuation of an analytic function $f$ in terms of the geometric rate of convergence on a compact set of sequences of multi-point rational interpolants of $f$. The rational approximants have a…
A C++ software design is presented that can be used to interpolate data in any number of dimensions. The design is based on a combination of templates of functional collections of elements and so-called type lists. The design allows for…
We build a multifractal object and use it as a support to study percolation. We identify some differences between percolation in a multifractal and in a regular lattice. We use many samples of finite size lattices and draw the histogram of…
In this paper, we study how to quickly compute the <-minimal monomial interpolating basis for a multivariate polynomial interpolation problem. We address the notion of "reverse" reduced basis of linearly independent polynomials and design…
In this work, we study superconvergence properties for some high-order orthogonal polynomial interpolations.The results are two-folds: When interpolating function values, we identify those points where the first and second derivatives of…
The multivariate regression model basically offers the analysis of a single dataset with multiple responses. However, such a single-dataset analysis often leads to unsatisfactory results. Integrative analysis is an effective method to pool…
We consider regular polynomial interpolation algorithms on recursively defined sets of interpolation points which approximate global solutions of arbitrary well-posed systems of linear partial differential equations. Convergence of the…