Fast wavelet transforms and numerical algorithms. I. (English) Zbl 0722.65022

Beylkin, G.; Coifman, R.; Rokhlin, V.

Commun. Pure Appl. Math. 44, No. 2, 141-183 (1991).

Based on the theory of wavelets, methods for the fast numerical application of linear operators to arbitrary vectors are presented. These methods are applicable to all Calderón-Zygmund and pseudo-differential operators.

Reviewer: V.Mehrmann (Bielefeld)

MSC:

65T60	Numerical methods for wavelets
65F30	Other matrix algorithms (MSC2010)
65D32	Numerical quadrature and cubature formulas
65T50	Numerical methods for discrete and fast Fourier transforms
42C40	Nontrigonometric harmonic analysis involving wavelets and other special systems

Keywords:

fast wavelet transforms; algorithms; fast Fourier transform; wavelets; matrix vector; multiply Haar system; Calderón-Zygmund operators; wavelets based quadrature; integral operators; pseudo-differential operators

References:

[1]	and , A Fast Algorithm for the Evaluation of Legendre Expansions, Yale University Technical Report, YALEU/DCS/RR-671, 1989.
[2]	Carrier, SIAM J. Sci. Stat. Comp. 9 pp 669– (1988)
[3]	and , Nonlinear Harmonic Analysis, Operator Theory, and P.D.E., Ann. Math. Studies, E. Stein, ed., Princeton, 1986
[4]	Daubechies, Comm. Pure Appl. Math 41 pp 909– (1988)
[5]	Greengard, J. Comp. Phys. 73 pp 325– (1987)
[6]	Mallat, Technical Report 412 (1988)
[7]	Meyer, Séminaire Bourbaki 662 (1985–86)
[8]	Wavelets and operators, in Analysis at Urbana, Vol. 1, , and , eds., London Math. Soc., Lecture Notes Series 137, 1989, pp. 256–365. · doi:10.1017/CBO9780511662294.012
[9]	and , 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.
[10]	A modified Haar system and higher order spline systems, Conf. in Harmonic Analysis in honor of Antoni Zygmund, Wadworth Math. Series II, et al., eds., pp. 475–493.