The Petrov-Galerkin method for second kind integral equations .2. Multiwavelet schemes

This paper continues the theme of the recent work [3] and further develops the Petrov-Galerkin method for Fredholm integral equations of the second kind. Specifically, we study wavelet Petrov-Galerkin schemes based on discontinuous orthogonal multiwavelets and prove that the condition number of the coefficient matrix for the linear system obtained from the wavelet Petrov-Galerkin scheme is bounded. In addition, we propose a truncation strategy which forms a basis for fast wavelet algorithms and analyze the order of convergence and computational complexity of these algorithms.