Fast Dense Matrix Method for the Solution of Integral Equations of the Second Kind

Hon Fu Raymond CHAN, Fu-Rong LIN, Wing-Fai NG

Research output: Journal PublicationsJournal Article (refereed)peer-review


We present a fast algorithm based on polynomial interpolation to approximate matrices arising from the discretization of second-kind integral equations where the kernel function is either smooth, non-oscillatory and possessing only a finite number of singularities or a product of such function with a highly oscillatory coefficient function. Contrast to wavelet-like approximations, our approximation matrix is not sparse. However, the approximation can be construced in O(n) operations and requires O(n) storage, where n is the number of quadrature points used in the discretization. Moreover, the matrix-vector multiplication cost is of order O(nlogn). Thus our scheme is well suitable for conjugate gradient type methods. Our numerical results indicate that the algorithm is very accurate and stable for high degree polynomial interpolation.
Original languageEnglish
Pages (from-to)105-120
Number of pages16
JournalNumerical Mathematics
Issue number1
Publication statusPublished - May 1998
Externally publishedYes


  • Fredholm integral equation
  • polynomial interpolation


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