The state-covariance of a linear filter is characterized by a certain algebraic commutativity property with the state matrix of the filter, and also imposes a generalized interpolation constraint on the power spectrum of the input process. This algebraic property and the relationship between state-covariance and the power spectrum of the input allow the use of matrix pencils and analytic interp...

The noise sensitivity of interpolation and extrapolation matrices is investigated. For certain bandwidth and truncation parameters, the interpolation matrix is shown to yield results at a lower noise level than the input data. The input noise level, however, can be lowered by filtering the result. The noise level in the interpolated interval is shown to be lower near where the image is known. T...

Submitted for the MAR16 Meeting of The American Physical Society Spectral Gauss quadrature method with subspace interpolation for Kohn-Sham Density functional theory XIN WANG, US Army Rsch Lab Aberdeen — Algorithms with linear-scaling (O(N )) computational complexity for Kohn-Sham density functional theory (K-S DFT) is crucial for studying molecular systems beyond thousands of atoms. Of the O(N...

In this work we present a number of results concerning the nite dimensional band-limited interpolation problem. Our aim is to understand how the stability of the interpolation problem is aaected by changes in the positions of the interpolation knots. We give upper and lower bounds for the eigenvalues of the interpolation matrix, as functions of the gaps between missing samples. The upper bound ...

It is known that interpolation with radial basis functions of the same shape can guarantee a non-singular interpolation matrix, whereas little is known when one uses various shapes. In this paper, we prove that a class of compactly supported radial basis functions are convex on a certain region; based on this local convexity and ready local geometrical property of the interpolation points, we c...

In this paper‎, ‎we decide to select the best center nodes‎ ‎of radial basis functions by applying the Multiple Criteria Decision‎ ‎Making (MCDM) techniques‎. ‎Two methods based on radial basis‎ ‎functions to approximate the solution of partial differential‎ ‎equation by using collocation method are applied‎. ‎The first is based‎ ‎on the Kansa's approach‎, ‎and the second is based on the Hermit...

First, I would like to thank the author of ”Comments on ’A Simple and Accurate Algorithm for Barycentric Rational Interpolation’” (hereafter referred to as ”the comments”) for their interest in my work [1]. The author of the comments points out a novel relationship between barycentric rational interpolation, the Welch-Berlekamp key equation and Gröbner bases. This could turn out to be a very pr...

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-Padé approximation problem in [Van Barel and Bultheel, Numerical Algorithms 3, 1992] and the rational interpolation problem in [Beckermann and Labahn, SIAM J. Matrix Anal. Appl. 22, 2000]. Particular inst...

Various problems in pure and applied mathematics and engineering can be reformulated as linear algebra problems involving dense structured matrices. The structure of these dense matrices is understood in the sense that their n2 entries can be completeley described by a smaller number O(n) of parameters. Manipulating directly on these parameters allows us to design efficient fast algorithms. One...

We obtain necessary and sufficient conditions for NevanlinnaPick interpolation on the unit disk with the additional restriction that all analytic interpolating functions satisfy f ′(0) = 0. Alternatively, these results can be interpreted as interpolation results for H∞(V ), where V is the intersection of the bidisk with an algebraic variety. We use an analysis of C*-envelopes to show that these...