Fast solvers of integral equations of the second kind: wavelet methods
نویسندگان
چکیده
منابع مشابه
Fast solvers of integral equations of the second kind: wavelet methods
For the Fredholm integral equation u=T u+f on the real line, fast solvers are designed on the basis of a discretized wavelet Galerkin method with the Sloan improvement of the Galerkin solution. The Galerkin system is solved by GMRES or by the Gauss elimination method. Our concept of the fast solver includes the requirements that the parameters of the approximate solution un can be determined in...
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We use vector-valued multiwavelets on compact sets to develop a Galerkin method for systems of integral equations of the second kind. We propose a compression strategy for the coeflieient matrix of the linear system obtained from this method and show that the compressed scheme preserves almost optimal convergence rate of the original scheme and yields a sparse matrix with a bounded condition nu...
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An ecient method, based on the Legendre wavelets, is proposed to solve thesecond kind Fredholm and Volterra integral equations of Hammerstein type.The properties of Legendre wavelet family are utilized to reduce a nonlinearintegral equation to a system of nonlinear algebraic equations, which is easilyhandled with the well-known Newton's method. Examples assuring eciencyof the method and its sup...
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A class of vector-space bases is introduced for the sparse representation of discretiza-tions of integral operators. An operator with a smooth, nonoscillatory kernel possessing a finite number of singularities in each row or column is represented in these bases as a sparse matrix, to high precision. A method is presented that employs these bases for the numerical solution of second-kind integra...
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ژورنال
عنوان ژورنال: Journal of Complexity
سال: 2005
ISSN: 0885-064X
DOI: 10.1016/j.jco.2004.07.002