The Petrov–Galerkin method for second kind integral equations II: multiwavelet schemes
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This paper continues the theme of the recent work [Z. Chen and Y. Xu, The Petrov–Galerkin and iterated Petrov–Galerkin methods for second kind integral equations, SIAM J. Numer. Anal., to appear] 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.
KeywordsCond Condition Number Galerkin Method Wavelet Base Fredholm Integral Equation
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