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IEEE Transactions on Antennas and Propagation
Volume 47 Number 10, October 1999

Solution of Large Dense Complex Matrix Equations Utilizing Wavelet-Like Transforms

Page 1628.

Abstract:

This paper presents the wavelet-like transforms, which are quite different from the wavelet transform for the solution of large dense complex matrix equations. From a purely numerical standpoint, these wavelet-like transforms are not true orthogonal transforms as the condition number of the resulting matrix changes after the thresholding. These effects are illustrated through examples.

References

1. G. Beylkin, R. Coifman, and V. Rokhlin, "Fast wavelet transforms and numerical algorithms," Commun. Pure Appl. Math., vol. 44, pp. 141-183.
2. S. G. Mallat, "A theory for multiresolution signal decomposition: The wavelet representation," IEEE Trans., Pattern Anal. Machine Intell., vol. 11, pp. 674-693, July 1990.
3. B. Alpert, G. Beylkin, R. Coifman, and V. Rokhlin, "Wavelet-like base for the fast solution of second-kind integral equations," SIAM J. Sci. Comput., vol. 14, no. 1, pp. 159-184, 1993.
4. H. Kim and H. Ling, "On the application of fast wavelet transform to the integral equation solution of electromagnetic scattering problems," Microwave Opt. Technol. Lett., vol. 6, no. 3, pp. 168-173, Mar. 1993.
5. R. L. Wagner and W. C. Chew, "A study of wavelets for the solution of electromagnetic integral equations," IEEE Trans. Antennas Propagat., vol. 43, pp. 802-810, Aug. 1995.
6. B. Z. Steinberg and Y. Leviatan, "On the use of wavelet expansions in the method of moments," IEEE Trans. Antennas Propagat., vol. 41, pp. 610-619, Mar. 1993.
7. J. C. Goswami, A. K. Chan, and C. K. Chui, "On solving first-kind integral equations using wavelets on a bounded interval," IEEE Trans. Antennas Propagat., vol. 43, pp. 614-622, June 1995.
8. G. Wang, "A hybrid wavelet expansion and boundary element analysis of electromagnetic scattering from conducting objects," IEEE Trans. Antennas Propagat., vol. 43, pp. 170-178, Feb. 1995.
9. T. K. Sarkar et al., "A tutorial on wavelets from an electrical engineering perspective: Part I: Discrete wavelet techniques," IEEE Antennas Propagat. Mag., vol. 40, pts. I, II, pp. 173-197, Oct. 1998.
10. A. P. Calderon, "Intermediate spaces and interpolation, the complex method," Studies Math., vol. 24, pp. 113-190, 1964.
11. W. H. Press, S, Teukolsky, W. T. Vetterling, and B. P. Flemery, Numerical Recipes--The Art of Scientific Computing.Cambridge, U.K.: Cambridge Univ. Press, 1992.
12. G. Strang and T. Nguyen, Wavelet and Filter Banks.Cambridge, MA: Wellesley-Cambridge, 1996.