Представление вейвлет-преобразования с вейвлетами гауссова семейства суперпозицией решений дифференциальных уравнений в частных производных

E.B. Postnikov

The representation of a wavelet transform of the Gaussian family by a superposition of solutions to partial differential equations

Authors

E.B. Postnikov

Keywords:

непрерывные вейвлет-преобразования

вейвлет Морле

гауссовы вейвлеты

уравнение диффузии

уравнения в частных производных

Abstract

The usage of partial differential equations for the evaluation of a wavelet transform with real and complex wavelets and with vanishing higher moments is considered. Contrary to the case of the transform with the standard Morlet wavelet, the sought-for transform can be found as a superposition of solutions to several Cauchy problems with various initial values. These initial values are the products of a transformed function with some power functions whose exponents vary from zero to the maximal number of a vanishing moment.

Downloads

PDF (Русский)

Published

2008-03-15

Issue

Vol. 9 (2008): Issue 1.

Section

Section 1. Numerical methods and applications

Author Biography

E.B. Postnikov

Kursk State University,
Faculty of Physics and Mathematics

References

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Постников Е.Б. Вычисление непрерывного вейвлет-преобразования как решение задачи Коши для системы дифференциальных уравнений в частных производных // Ж. вычисл. матем. и матем. физики. 2006. 46, № 1. 77-82.
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How to cite

Demidova A.N. and Zhileikin Ya.M. A method for solving the problem of nonlinear optical self-focusing in an infinite half-space // Numerical Methods and Programming. 2008. 9, No 1. 77–83.

TEX CODE:

{\it Demidova~A.N.~and~Zhileikin~Ya.M.}
A method for solving the problem of nonlinear optical self-focusing in an infinite half-space~//
Numerical Methods and Programming. 2008.
\textbf{9}, No~1. 77--83.

Demidova A.  and Zhileikin Y. ,  (2008) “A method for solving the problem of nonlinear optical self-focusing in an infinite half-space,” Numerical Methods and Programming, vol. 9, no. 1, pp. 77–83.

TEX CODE:

Demidova~A.~ and~Zhileikin~Y.~, (2008)
``A method for solving the problem of nonlinear optical self-focusing in an infinite half-space,''
{\it Numerical Methods and Programming}, vol.~9, no.~1, pp.~77--83.

A.  Demidova and Y.  Zhileikin,  “A method for solving the problem of nonlinear optical self-focusing in an infinite half-space,” Numerical Methods and Programming 9, no. 1 (2008): 77–83

TEX CODE:

A.~ Demidova~and~Y.~ Zhileikin,
``A method for solving the problem of nonlinear optical self-focusing in an infinite half-space,''
{\it Numerical Methods and Programming}, no.~1 (2008): 77--83

Demidova A.  and Zhileikin Y.  A method for solving the problem of nonlinear optical self-focusing in an infinite half-space. Numerical Methods and Programming. 2008;9(1):77–83.(In Russ.).

TEX CODE:

Demidova~A.~ and~Zhileikin~Y.~
A method for solving the problem of nonlinear optical self-focusing in an infinite half-space.
Numerical Methods and Programming. 2008;9(1):77--83.(In Russ.).