Wavelets based on orthogonal polynomials
HTML articles powered by AMS MathViewer
- by Bernd Fischer and Jürgen Prestin PDF
- Math. Comp. 66 (1997), 1593-1618 Request permission
Abstract:
We present a unified approach for the construction of polynomial wavelets. Our main tool is orthogonal polynomials. With the help of their properties we devise schemes for the construction of time localized polynomial bases on bounded and unbounded subsets of the real line. Several examples illustrate the new approach.References
- T. S. Chihara, An introduction to orthogonal polynomials, Mathematics and its Applications, Vol. 13, Gordon and Breach Science Publishers, New York-London-Paris, 1978. MR 0481884
- C. K. Chui and H. N. Mhaskar, On trigonometric wavelets, Constr. Approx. 9 (1993), no. 2-3, 167–190. MR 1215768, DOI 10.1007/BF01198002
- Philip J. Davis, Interpolation and approximation, Blaisdell Publishing Co. [Ginn and Co.], New York-Toronto-London, 1963. MR 0157156
- B. Fischer, Polynomial based iteration methods for symmetric linear systems, Wiley-Teubner, Chichester, 1996.
- George Gasper, Banach algebras for Jacobi series and positivity of a kernel, Ann. of Math. (2) 95 (1972), 261–280. MR 310536, DOI 10.2307/1970800
- T. Kilgore and J. Prestin, Polynomial wavelets on the interval, Constr. Approx. 12 (1996), no. 1, 95–110. MR 1389921, DOI 10.1007/s003659900004
- Gerlind Plonka, Kathi Selig, and Manfred Tasche, On the construction of wavelets on a bounded interval, Adv. Comput. Math. 4 (1995), no. 4, 357–388. MR 1366509, DOI 10.1007/BF02123481
- Gabor Szegö, Orthogonal polynomials, American Mathematical Society Colloquium Publications, Vol. 23, American Mathematical Society, Providence, R.I., 1959. Revised ed. MR 0106295
- M. Tasche, Fast algorithms for discrete Chebyshev - Vandermonde transforms and applications, Numer. Alg. 5 (1993), 453–464.
- M. Tasche, Polynomial wavelets on $[-1,1]$, Approximation theory, wavelets and applications (Maratea, 1994) NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., vol. 454, Kluwer Acad. Publ., Dordrecht, 1995, pp. 497–512. MR 1340913
Additional Information
- Bernd Fischer
- Affiliation: Institut für Mathematik, Medizinische Universität zu Lübeck, D – 23560 Lübeck, Germany
- Email: fischer@informatik.mu-luebeck.de
- Jürgen Prestin
- Affiliation: Fachbereich Mathematik, Universität Rostock, D – 18051 Rostock, Germany
- Email: prestin@mathematik.uni-rostock.d400.de
- Received by editor(s): January 24, 1996
- Received by editor(s) in revised form: July 8, 1996
- © Copyright 1997 American Mathematical Society
- Journal: Math. Comp. 66 (1997), 1593-1618
- MSC (1991): Primary 42C05, 65D05
- DOI: https://doi.org/10.1090/S0025-5718-97-00876-4
- MathSciNet review: 1423073