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Wavelet Methods for Solving Integral Equations

The following sources are recommended by a professor whose research specialty is wavelet methods for solving integral equations.


Six Superlative Sources

· B.K. Alpert, A class of bases in L^2 for the sparse representatiion of integral operators, SIAM J. Math. Anal., 24 (1993), 246-262.

· G. Beylkin, R. Coifman, and V. Rokhlin, Fast wavelet transforms and numerical algorithms I, Comm. Pure and Appl. Math., 44 (1991), 14-183.

· W. Dahmen, S. Proessdorf, and R. Schneider, Wavelet approximation methods for pseudodifferential equations II: Matrix compression and fast algorithms, Adv. Comput. Math., 1 (1993), 259-335.

· C.A. Micchelli, Y. Xu, and Y. Zhao, Wavelet Galerkin methods for second-kind integral equations, J. Comput. Appl. Math., 86 (1997), 251-270.

· A. Rathsfeld, A wavelet algorithm for the solution of the double layer potential equation over polygonal boundaries, J. Int. Equations Appl., 7 (1994), 47-98.

· T. von Petersdorf, and C. Schwab, Wavelet approximations for first kind boundary integral equations on polygons, Numer. Math. 74 (1996), 479-519.

Other Excellent Sources

· B. Alpert, G. Beylkin, R. Coifman, and V. Roklin, Waveletlike bases for the fast solution of second-kind integral equations, SIAM J. Sci. Statist. Comput., 14 (1993), 159-184.

· G. Beylkin, On the representation of operators in bases on compactly supported wavelets, SIAM J. Numer. Anal. 29 (1992), 1716-1740.

· Z. Chen, C.A. Micchelli, and Y. Xu, The Petrov-Kalerkin method for second kind integral equations II: multiwavelet schemes, Adv. Comput. Math. 7 (1997), 199-233.

· W. Dahmen, Wavelet and multiscale methods for operator equations, Acta Numerica (1997), 55-228.

· A. Rathsfeld, A wavelet algorithm for the boundary element solution of a geodetic boundary value problem, Comput. Methods Appl. Mech. Engrg. 157 (1998), 267-287.

· T. von Petersdorff, C. Schwab, and R. Schneider, Multiwavelets for second-kind integral equations, SIAM J. Numer. Anal. 34 (1997), 2212-2227.

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