Title | **Construction of orthonormal wavelets using symbolic algebraic methods.** |

Author(s) | Vaclav Finvek, Dana vCerna |

Type | Book, Chapter in Book, Conference Proceeding |

Abstract | Our contribution is concerned with the solution of nonlinear algebraic equations systems arising from the computation of scaling coefficients of orthonormal wavelets with compact support. Specifically Daubechies wavelets, symmlets, coiflets, and generalized coiflets. These wavelets are defined as a solution of equation systems which are partly linear and partly nonlinear. The idea of presented methods consists in replacing those equations for scaling coefficients by equations for scaling moments. It enables us to eliminate some quadratic conditions in the original system and then simplify it. The simplified system is solved with the aid of the Gröbner basis method. The advantage of our approach is that in some cases, it provides all possible solutions and these solutions can be computed to arbitrary precision. For small systems, we are even able to find explicit solutions. The computation was carried out by symbolic algebra software Maple. |

ISBN | 978-0-7354-0708-4/hbk; 978-0-7 |

URL |
http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.3241329 |

Language | English |

Pages | 1333--1336 |

Publisher | Melville, NY: American Institute of Physics (AIP) |

Year | 2009 |

Edition | 0 |

Translation |
No |

Refereed |
No |