Biomedical Imaging Group

Student Project: Sylvia Garcia

Sylvia Garcia | Semester project |

Section Mathematiques, EPFL | June 1999 |

CONTENTS

We extend some earlier results on the approximation properties of a large class of operators that approximates a function into an integer-shift
invariant space in *L ^{2}* by projection of the function. Concretely we work out a Fourier analysis method that
applies to the

These results can be applied an analysis of the accuracy of the approximation using finite elements, as is shown in the second half of the paper. In particular we obtain asymptotic constants for Legendre and Hermite finite elements and show that spline approximation yelds better results in this respect.

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