Closed-Form Projection Method for Regularizing a Function Defined by a Discrete Set of Noisy Data and for Estimating its Derivative and Fractional Derivative

Timothy J. Burns; Bert W. Rust

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arXiv · 1805.09849

Closed-Form Projection Method for Regularizing a Function Defined by a Discrete Set of Noisy Data and for Estimating its Derivative and Fractional Derivative

Timothy J. Burns·Bert W. Rust

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Abstract

We present a closed-form finite-dimensional projection method for regularizing a function defined by a discrete set of measurement data, which have been contaminated by random, zero mean errors, and for estimating the derivative and fractional derivative of this function by linear combinations of a few low degree trigonometric or Jacobi polynomials. Our method takes advantage of the fact that there are known infinite-dimensional singular value decompositions of the operators of integration and fractional integration.

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Timothy J. Burns, Bert W. Rust. 2018-05-24. Closed-Form Projection Method for Regularizing a Function Defined by a Discrete Set of Noisy Data and for Estimating its Derivative and Fractional Derivative. https://arxiv.org/abs/1805.09849

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