A Quadrature Formula Based On Sampling In Meyer Wavelet Subspaces

Xiaoping Shen1
1Department of Mathematics, Eastern Connecticut State University, Willimantic

Tóm tắt

In this paper we discuss a weighted trapezoidal rule based on sampling in Meyer wavelet subspaces. For a wide class of functions, we obtain convergence and error bounds. Some examples are given to construct sampling functions.

Tài liệu tham khảo

P. J. Davis and P. Rabinowitz, Methods of Numerical Integration, 2nd edn., Academic Press, New York, 1984. N. Eggert and J. Lund, The trapezoidal rule for analytic functions of rapid decrease, J. Comput. Appl. Math. 27, 389–406 (1989). G. Evans, Practical Numerical Integration, Wiley, New York, 1993. N. Eggert and K. Bowers, Sinc Methods For Quadrature and Differential Equations, SIAM, Philadelphia, 1992. C. Rappier and P. Olivier, A quadrature formula involving zeros of Bessel functions, Math. Comp. 60, 303–316 (1993). G. Grozev and Q. Rahman, A quadrature formula with zeros of Bessel functions as nodes, Math. Comp. 64, 715–725 (1995). F. Stenger, Numerical Methods Based on Sinc and Analytic Functions, Springer Verlag, New York, 1993 G. G. Walter, Wavelets and Other Orthogonal Wavelets with Applications, CRC Press, Boca Raton, FL, 1994. G. G. Walter, Wavelet subspaces with an oversampling property, Indag. Math., [N.S.], 4, 499–507 (1993). R. Wong, Asymptotic Approximations of Integrals, Academic Press, New York, 1989. A. I. Zayed, Advances in Shannon Sampling Theory, CRC Press, Boca Raton, FL, 1993.