| FAST DENSE MATRIX METHOD FOR THE SOLUTION OF INTEGRAL EQUATIONS OF THE SECOND KIND |
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| 引用本文： | 陈汉夫,林福荣,吴荣辉. FAST DENSE MATRIX METHOD FOR THE SOLUTION OF INTEGRAL EQUATIONS OF THE SECOND KIND[J]. 高等学校计算数学学报(英文版), 1998, 0(1) |
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| 作者姓名： | 陈汉夫 林福荣 吴荣辉 |
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| 作者单位： | Raymond H. Chan Department of Mathematics，Chinese University of Hong Kong Shatin，Hong KongFu-rong Lin Department of Mathematics，Chinese University，Shantou 515063，PRCWing-fai Ng Department of Mathematics，Chinese University of Hong Kong Shatin，Hong Kong |
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| 基金项目： | Research supported in part by Hong Kong Research Grant Council grats no.CUHK178/83E |
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| 摘 要： | 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, ourapproximation 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.
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FAST DENSE MATRIX METHOD FOR THE SOLUTION OF INTEGRAL EQUATIONS OF THE SECOND KIND |
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| Raymond H. Chan. FAST DENSE MATRIX METHOD FOR THE SOLUTION OF INTEGRAL EQUATIONS OF THE SECOND KIND[J]. Numerical Mathematics A Journal of Chinese Universities English Series, 1998, 0(1) |
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| Authors: | Raymond H. Chan |
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| Affiliation: | Raymond H. Chan Department of Mathematics,Chinese University of Hong Kong Shatin,Hong KongFu-rong Lin Department of Mathematics,Chinese University,Shantou 515063,PRCWing-fai Ng Department of Mathematics,Chinese University of Hong Kong Shatin,Hong Kong |
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| Abstract: | 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. |
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| Keywords: | Fredholm integral equation polynomial interpolation. |
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