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Minimum Principles for Ill-Posed Problems

Franklin, Joel N. (1978) Minimum Principles for Ill-Posed Problems. SIAM Journal on Mathematical Analysis, 9 (4). pp. 638-650. ISSN 0036-1410. doi:10.1137/0509044.

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Ill-posed problems Ax = h are discussed in which A is Hermitian,and postive definite; a bound ║Bx║ ≤ β is prescribed. A minimum principle is given for an approximate solution x^. Comparisons are made with the least-squares solutions of K. Miller, A. Tikhonov, et al. Applications are made to deconvolution, the backward heat equation, and the inversion of ill-conditioned matrices. If A and B are positive-definite, commuting matrices, the approximation x^ is shown to be about as accurate as the least-squares solution and to be more quickly and accurately computable.

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Additional Information:© 1978 Society for Industrial and Applied Mathematics. Received by the editors October 15, 1976, and in revised form July 28, 1977.
Issue or Number:4
Record Number:CaltechAUTHORS:FRAsiamjma78
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13072
Deposited On:03 Feb 2009 19:29
Last Modified:08 Nov 2021 22:35

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