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Convergence of a generalized pulse-spectrum technique (GPST) for inverse problems of $ 1$-D diffusion equations in space-time domain


Authors: X. Y. Liu and Y. M. Chen
Journal: Math. Comp. 51 (1988), 477-489
MSC: Primary 65P05; Secondary 35R30
MathSciNet review: 958636
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Abstract: The problem of convergence of a special form of the generalized pulse-spectrum technique (GPST) for solving inverse problems of one-dimensional diffusion equations in space-time domain is considered. Under the assumptions that a Tikhonov regularized solution exists and the derivative operator of the regularized forward problem at the regularized solution is invertible, the iterative solutions of this special GPST converge to the Tikhonov regularized solution in C norm if the initial guess is close enough to the Tikhonov regularized solution and the rate of convergence is at least linear.


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DOI: https://doi.org/10.1090/S0025-5718-1988-0958636-8
Article copyright: © Copyright 1988 American Mathematical Society