Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext. 32700
Fax: 519-746-4319
PDF files require Adobe Acrobat Reader
MC 5501
Kirill Serkh, Department of Mathematics, University of Toronto
The Approximation of Singular Functions by Series of Non-integer Powers
In this talk, we describe an algorithm for approximating functions of the form $f(x) = \langle \sigma(\mu),x^\mu \rangle$ over the interval $[0,1]$, where $\sigma(\mu)$ is some distribution supported on $[a,b]$, with $0<a<b<\infty$. Given a desired accuracy and the values of $a$ and $b$, our method determines a priori a collection of non-integer powers, so that functions of this form are approximated by expansions in these powers, and a set of collocation points, such that the expansion coefficients can be found by collocating a given function at these points. Our method has a small uniform approximation error which is proportional to the desired accuracy multiplied by some small constants, and the number of singular powers and collocation points grows logarithmically with the desired accuracy.
Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext. 32700
Fax: 519-746-4319
PDF files require Adobe Acrobat Reader
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