| A QUASI-NEWTON METHOD IN INFINITE-DIMENSIONAL SPACES AND ITS APPLICATION FOR SOLVING A PARABOLIC INVERSE PROBLEM |
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| 作者单位： | Department of Mathematics，Tianjin University，Tianjin 300072，P.R. China. |
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| 摘 要： | 1.IntroductionQuasi-Newtonmethodsplayanimportantroleinnumericallysolvingnon--linearsystemsofequationsontheEuclideanspaces.Blltitseemsthatthequasi-Newtonmethodshavenotbeenapplieddirectlytosolvinginverseproblemsinpartialdifferentialequations(PDE)uptonowifwe…
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A QUASI-NEWTON METHOD IN INFINITE-DIMENSIONAL SACES AND ITS APPLICATION FOR SOLVING A PARABOLIC INVERSE PROBLEM |
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| Wen-huan Yu. A QUASI-NEWTON METHOD IN INFINITE-DIMENSIONAL SACES AND ITS APPLICATION FOR SOLVING A PARABOLIC INVERSE PROBLEM[J]. Journal of Computational Mathematics, 1998, 0(4) |
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| Authors: | Wen-huan Yu |
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| Abstract: | A Quasi-Newton method in Infinite-dimensional Spaces (QNIS) for solving operator equations is presellted and the convergence of a sequence generated by QNIS is also proved in the paper. Next, we suggest a finite-dimensional implementation of QNIS and prove that the sequence defined by the finite-dimensional algorithm converges to the root of the original operator equation providing that the later exists and that the Frechet derivative of the governing operator is invertible. Finally, we apply QNIS to an inverse problem for a parabolic differential equation to illustrate the efficiency of the finite-dimensional algorithm. |
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| Keywords: | Quasi-Newton method parabolic differential equation inverse problems in partial differential equations linear and Q-superlinear rates of convergence |
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