The Petrov-Galerkin Method for Second Kind Integral Equations II: Multiwavelet Schemes

This paper continues the theme of the recent work (CX) and further develops the Petrov-Galerkin method for Fredholm integral equations of the second kind. Specifically, we study wavelet Petrov-Galerkin schems based on descontinuous orthogonal multiwavelets and prove that 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.