A multiresolution approach to regularization of singular operators and fast summation

SIAM Journal on Scientific Computing

Volumn 24, Issue 1, 2003, Pages 81-117

  Beylkin, Gregory ^a   Cramer, Robert ^a  

^a UNIVERSITY OF COLORADO   (United States)

Author keywords

Integral equations; Integral operators; Integral transforms; Multiresolution analysis; n body problems; Regularization; Wavelets

Indexed keywords

ALGORITHMS; CONVOLUTION; INTEGRAL EQUATIONS; MATHEMATICAL OPERATORS; WAVELET TRANSFORMS;

INTEGRAL OPERATORS; INTEGRAL TRANSFORMS; MULTIRESOLUTION ANALYSIS; REGULARIZATION;

COMPUTATIONAL METHODS;

EID: 0037250788     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827500379227     Document Type: Article

References (16)

1. 2 for the sparse representation of integral operators, SIAM J. Math. Anal., 24 (1993), pp. 246-262.
2. B. Alpert, G. Beylkin, R. Coifman, and V. Rokhlin, Wavelet-like bases for the fast solution of second-kind integral equations, SIAM J. Sci. Comput., 14 (1993), pp. 159-184.
3. C. Anderson, A method of local corrections for computing the velocity field due to a distribution of vortex blobs, J. Comput. Phys., 62 (1986), pp. 111-123.
4. G. Beyklin, On the representation of operators in bases of compactly supported wavelets, SIAM J. Numer. Anal., 6 (1992), pp. 1716-1740.
5. G. Beylkin, R. Coifman, and V. Rokhlin, Fast wavelet transforms and numerical algorithms I, Comm. Pure Appl. Math., 44 (1991), pp. 141-183.
6. H. Cheng, L. Greengard, and V. Rokhlin, A fast adaptive multipole algorithm in three dimensions, J. Comput. Phys., 155 (1999), pp. 468-498.
7. C. K. Chui, An Introduction to Wavelets, Academic Press, Boston, MA, 1992.
8. A. Cohen, I. Daubechies, and J. Feauveau, Biorthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math., 45 (1992), pp. 485-560.
9. I. Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, 1992.
10. I. Gel'Fand and G. Shilov, Generalized Functions, Vol. 1, Academic Press, New York, 1964.
11. L. Greengard, and V. Rokhlin, A fast algorithm for particle simulations, J. Comput. Phys., 73 (1987), pp. 325-348.
12. J. Jackson, Classical Electrodynamics, Wiley, New York, 1962.
13. P. Kolm and V. Rokhlin, Numerical quadratures for singular and hypersingular integrals, Comput. Math. Appl., 41 (2001), pp. 327-352.
14. W. Lawton, Necessary and sufficient conditions for constructing orthonormal wavelet bases, J. Math. Phys., 1 (1991), pp. 57-61.
15. Y. Meyer, Wavelets and Operators, Cambridge Stud. Adv. Math. 37, Cambridge University Press, Cambridge, 1992.
16. L. Schwartz, Théorie des distributions, Hermann, Paris, 1966.