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   -> Volume 6, Issue 5


Preprint: Connection Coefficients on Bounded Intervals
 
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"Charles H. Romine" (rominech@ornl.gov)
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PostPosted: Wed Apr 23, 1997 5:02 pm    
Subject: Preprint: Connection Coefficients on Bounded Intervals
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#4 Preprint: Connection Coefficients on Bounded Intervals

Barry Peyton and I would like to announce the availability of a
technical report describing the computation of connection coefficients
of compactly supported wavelets on bounded intervals. Our technique
permits the natural imposition of boundary conditions for PDEs on
bounded domains. The URL and abstract are given below. Thank you.

http://www.epm.ornl.gov/~romine/propercc.ps

Abstract

Daubechies wavelet basis functions have many properties that make them
desirable as a basis for a Galerkin approach to solving PDEs: they are
orthogonal, with compact support, and their connection coefficients
can be computed. The method developed by Latto et al. to compute
connection coefficients does not provide the correct inner product
near the endpoints of a bounded interval, making the implementation of
boundary conditions problematic. Moreover, the highly oscillatory
nature of the wavelet basis functions makes standard numerical
quadrature of integrals near the boundary impractical. We extend the
method of Latto et al. to construct and solve a linear system of
equations whose solution provides the exact computation of the
integrals at the boundaries. As a consequence, we provide the correct
inner product for wavelet basis functions on a bounded interval.
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