document: Wavelet collocation methods for a first kind boundary integral equation in acoustic scattering In this paper we consider a wavelet algorithm for the piecewise constant collocation method applied to the boundary element solution of a first kind integral equation arising in acoustic scattering . The conventional stiffness matrix is transformed into the corresponding matrix with respect to wavelet bases , and it is approximated by a compressed matrix . Finally , the stiffness matrix is multiplied by diagonal preconditioners such that the resulting matrix of the system of linear equations is well conditioned and sparse . Using this matrix , the boundary integral equation can be solved effectively
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