Vector extrapolation enhanced TSVD for linear discrete ill-posed problems
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The truncated singular value decomposition (TSVD) is a popular solution method for small to moderately sized linear ill-posed problems. The truncation index can be thought of as a regularization parameter; its value affects the quality of the computed approximate solution. The choice of a suitable value of the truncation index generally is important, but can be difficult without auxiliary information about the problem being solved. This paper describes how vector extrapolation methods can be combined with TSVD, and illustrates that the determination of the proper value of the truncation index is less critical for the combined extrapolation-TSVD method than for TSVD alone. The numerical performance of the combined method suggests a new way to determine the truncation index.
KeywordsIll-posed problem Truncated singular value decomposition Vector extrapolation Truncation criterion
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- 6.Brezinski, C., Rodriguez, G., Seatzu, S.: Error estimates for linear systems with applications to regularization. Numer. Algorithms (in press)Google Scholar
- 8.Eddy, R.P.: Extrapolation to the limit of a vector sequence. In: Wang, P.C.C. (ed.) Information Linkage Between Applied Mathematics and Industry, pp. 387–396. Academic Press, New York (1979)Google Scholar
- 10.Gander, W., Golub, G.H., Gruntz, D.: Solving linear equations by extrapolation. In: Kovalic, J.S. (ed.) Supercomputing, Nato ASI Series F: Computer and Systems Sciences, vol. 62, pp. 279–293. Springer, Berlin (1989)Google Scholar
- 14.Hansen, P.C.: Rank-Deficient and Discrete Ill-Posed Problems. SIAM, Philadelphia (1998)Google Scholar