In this work, the question of the coherency matrix propagation of a light beam is addressed by means of the analysis of interpolation processes between two physical situations. These physical situations are defined according to the second order statistical properties of the underlying process. Two states of a light beam or the path in a medium to go from a physical situation at distance z(1) to...

The nondegenerate Nevanlinna-Pick-Carathéodory-Fejer interpolation problem with finitely many interpolation conditions always has infinitely many solutions in a generalized Schur class Sκ for every κ ≥ κmin where the integer κmin equals the number of negative eigenvalues of the Pick matrix associated to the problem and completely determined by interpolation data. A linear fractional description...

This paper presents a computational technique that called Tau-collocation method for the developed solution of non-linear integro-differential equations which involves a population model. To do this, the nonlinear integro-differential equations are transformed into a system of linear algebraic equations in matrix form without interpolation of non-poly-nomial terms of equations. Then, using coll...

A novel small-animal SPECT imager, FastSPECT II, was recently developed at the Center for Gamma-Ray Imaging. FastSPECT II consists of two rings of eight modular scintillation cameras and list-mode data-acquisition electronics that enable stationary and dynamic imaging studies. The instrument is equipped with exchangeable aperture assemblies and adjustable camera positions for selections of magn...

A computational package has been developed to solve the bounded vibrational Schrödinger equation for up to three coupled coordinates on any given effective potential energy surface (PES) [1]. This article presents a new and improved version of the package with a fully automated point-wise PES evaluation as well as a revised routine for the computation of the Wilson G-matrix on scattered surface...

For interpolation of scattered multivariate data by radial basis functions, an \uncertainty relation" between the attainable error and the condition of the interpolation matrices is proven. It states that the error and the condition number cannot both be kept small. Bounds on the Lebesgue constants are obtained as a byproduct. A variation of the Narcowich{Ward theory of upper bounds on the norm...

SUMMARY A multiscale algorithm for the problem of optimal statistical interpolation of the observed data has been developed. This problem includes the calculation of the vector of the \analyzed" (best estimated) atmosphere ow eld w a by the formula w a = w f + P f H T y; where the quantity y is deened by the equation using the given model forecast rst guess w f and the vector of observations w ...

When a mesh of simplicial elements (triangles or tetrahedra) is used to form a piecewise linear approximation of a function, the accuracy of the approximation depends on the sizes and shapes of the elements. In finite element methods, the conditioning of the stiffness matrices also depends on the sizes and shapes of the elements. This article explains the mathematical connections between mesh g...

ABSTILACT: The problem is considered of passing from interpolation data for a real rational trarlsfer function matrix to a ~ninintal skate variable realization of the transfer function matrix. The tool is a Loewner matrix, which is a generalization of the standard Mankel matrix of linear s y s tetn realization theory, and which possesses a decompositioil into a product of generalized observabil...

A multiscale algorithm for the problem of optimal statistical interpolation of the observed data has been developed. This problem includes the calculation of the vector of the \analyzed" (best estimated) atmosphere ow eld w a by the formula w a = w f + P f H T y; where the quantity y is deened by the equation using the given model forecast rst guess w f and the vector of observations w o. H is ...