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Fast Algorithms for Calderón–Zygmund Singular Integral Operators

✍ Scribed by Yang Qi Xiang

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
186 KB
Volume
3
Category
Article
ISSN
1063-5203

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✦ Synopsis

Many people would say that Calderón-Zygmund operators have almost diagonal matrices in orthonormal wavelet bases. We will show that this statement is not true as stated. In contrast, the "nonstandard matrix representation" of Calderón-Zygmund operators always yields almost diagonal matrices. The Beyklin-Coifman-Rokhlin fast algorithm amounts to replacing these almost diagonal matrices by banded ones. We compute the operator norm of the error term in this approximation and give sharp estimates.

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