Volume 24, pp. 1-6, 2006.

Orthogonal least squares solutions for linear operators

Eva Acosta


This paper solves the problem of finding, in a least squares sense, the coefficients of a series expansion of a function in terms of a chosen orthogonal basis from the knowledge not of the function itself but from the action of a linear operator upon it. The coefficiens are evaluated by inner product with a set of functions related to the orthogonal basis through the adjoint operator of the linear operator. Examples for both differential operators and integral ones as well as related properties are given.

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Key words

orthogonal polynomials, linear operators, gradient operator, Radon transform

AMS subject classifications

33C90, 33C47, 42C05, 42C15, 47A05

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