Computation of connection coefficients and measure modifications for orthogonal polynomials
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We formulate and derive a generalization of an orthogonal rational-function basis for spectral expansions over the infinite or semi-infinite interval. The original functions, first presented by Wiener, are a mapping and weighting of the Fourier basis to th ...
In this project, we study and compare two methods to solve stochastic ordinary differential equations. The first is the Monte Carlo method and the second uses Polynomial Chaos. In the first part, we will solve a stochastic ordinary differential equation by ...
In this work we first focus on the Stochastic Galerkin approximation of the solution u of an elliptic stochastic PDE. We rely on sharp estimates for the decay of the coefficients of the spectral expansion of u on orthogonal polynomials to build a sequence ...
In this paper we propose and analyze a stochastic collocation method for solving the second order wave equation with a random wave speed and subjected to deterministic boundary and initial conditions. The speed is piecewise smooth in the physical space and ...
We address the problem of exact complex-wave reconstruction in digital holography. We show that, by confining the object-wave modulation to one quadrant of the frequency domain, and by maintaining a reference-wave intensity higher than that of the object, ...
In this paper, we show that the sum rules for generalized Hermite polynomials derived by Daboul and Mizrahi (2005 J. Phys. A: Math. Gen. 38 427-48) and by Graczyk and Nowak (2004 C. R. Acad. Sci., Ser. 1 338 849) can be interpreted and easily recovered usi ...
It is well known that transfer polynomials play an important role in the network code design problem. In this paper we provide a graph theoretical description of the terms of such polynomials. We consider acyclic networks with arbitrary number of receivers ...
In this paper we propose and analyze a stochastic collocation method for solving the second order wave equation with a random wave speed and subjected to deterministic boundary and initial conditions. The speed is piecewise smooth in the physical space and ...
It is well known that transfer polynomials play an important role in the network code design problem. In this paper we provide a graph theoretical description of the terms of such polynomials. We consider acyclic networks with arbitrary number of receivers ...
We study a multichannel sampling scheme, where different channels observe scaled and shifted versions of a common bandlimited signal. The channel gains and offsets are unknown a priori, and each channel samples at sub-Nyquist rates. This setup appears in m ...