Fast algorithms for problems on thermal tomography
Refereed conference paper presented and published in conference proceedings

香港中文大學研究人員

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摘要In this paper, we study an ill-posed, nonlinear inverse problem in heat conduction and hydrology applications. In [2], the problem is linearized to give a linear integral equation, which is then solved by the Tikhonov method with the identity as the regularization operator. We prove in this paper that the resulting equation is well-condition and has clustered spectrum. Hence if the conjugate gradient method is used to solve the equation, we expect superlinear convergence. However, we note that the identity operator does not give good solution to the original equation in general. Therefore in this paper, we use the Laplacian operator as the regularization operator instead. With the Laplacian operator, the regularized equation is ill-conditioned and hence a preconditioner is required to speed up the convergence rate if the equation is solved by the conjugate gradient method. We here propose to use the Laplacian operator itself as preconditioner. This preconditioner can be inverted easily by fast sine-transforms and we prove that the resulting preconditioned system is well-conditioned and has clustered spectrum too. Hence the conjugate gradient method converges superlinearly for the preconditioned system. Numerical results are given to illustrate the fast convergence.
著者Chan R.H., Cheung C.-P., Sun H.-W.
會議名稱1st International Workshop on Numerical Analysis and its Applications, WNAA 1996
會議開始日24.06.1996
會議完結日26.06.1996
會議地點Rousse
會議國家/地區保加利亞
出版年份1997
月份1
日期1
卷號1196
出版社Springer Verlag
出版地Germany
頁次90 - 97
國際標準書號3540625984
國際標準期刊號1611-3349
語言英式英語

上次更新時間 2020-07-09 於 01:42