Fast wavelet transforms and numerical algorithms I
Tóm tắt
A class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors. Previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices. In contrast, the methods presented here are based on the recently developed theory of wavelets and are applicable to all Calderon‐Zygmund and pseudo‐differential operators. The algorithms of this paper require order
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Tài liệu tham khảo
Alpert B. andRokhlin V. A Fast Algorithm for the Evaluation of Legendre Expansions Yale University Technical Report YALEU/DCS/RR‐671 1989.
Coifman R. andMeyer Y. Nonlinear Harmonic Analysis Operator Theory and P.D.E. Ann. Math. Studies E. Stein ed. Princeton 1986
Greengard L., 1987, A fast algorithm for particle simulations, J. Comp. Phys., 73, 325, 10.1016/0021-9991(87)90140-9
Mallat S., 1988, Review of Multifrequency Channel Decomposition of Images and Wavelet Models, Technical Report, 412
Meyer Y., 1985, Principe d'incertitude, bases Hilbertiennes et algèbres d'opérateurs, Séminaire Bourbaki, 662
O'Donnel S. T. andRokhlin V. A Fast Algorithm for the Numerical Evaluation of Conformation Mappings Yale University Technical Report YALEU/DSC/RR‐554 1987 SIAM J. Sci. Stat. Comp. 1989 pp.475–487.
Stromberg J. O., A modified Haar system and higher order spline systems, Conf. in Harmonic Analysis in honor of Antoni Zygmund, 475