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Solution of large dense complex matrix equations utilizing wavelet-like transforms

Solution d’équations à matrices complexes denses à l’aide de transformations de type ondelettes

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Abstract

The objective of this paper is to explore the validity of various mathematical properties of the wavelet-like transforms for the solution from thin wire structures utilizing the conventional integral equation technique based on the method of moments. It is illustrated through numerical experimentation that the conventional mathematical bounds existing for the classical wavelet transform do not apply to the wavelet-like transforms. Also the classical wavelet transform is really not applicable for the solution of the matrix equations. These statements will be illustrated through examples.

Résumé

Cet article explore la pertinence des diverses propriétés mathématiques des transformations de type ondelettes appliquées à la résolution d’équations matricielles complexes et denses d’ordre élevé. Ces équations interviennent dans l’étude de la diffraction d’ondes électromagnétiques par une structure filaire mince lorsqu’on utilise une technique d’équation intégrale fondée sur la méthode des moments. Une expérience numérique illustre que les limites mathématiques existant pour la transformation en ondelettes. De même, on montre que la transformation classique n’est pas vraiment applicable à la solution des équations matricielles. Toutes ces assertions sont illustrées par des exemples.

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Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Syracuse University, 13244-1240, Syracuse, New York

    Tapan K. Sarkar & Chaowei Su

  2. Dept. Senales and Sistemas, Polytechnique University of Madrid, 28040, Madrid

    Magdalena Salazar Palma

Authors
  1. Tapan K. Sarkar
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  2. Chaowei Su
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  3. Magdalena Salazar Palma
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Sarkar, T.K., Su, C. & Palma, M.S. Solution of large dense complex matrix equations utilizing wavelet-like transforms. Ann. Télécommun. 54, 56–67 (1999). https://doi.org/10.1007/BF02998647

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  • DOI: https://doi.org/10.1007/BF02998647

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