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Convergence of a Generalized Pulse-Spectrum Technique (GPST) for Inverse Problems of 1-D Diffusion Equations in Space-Time Domain

X. Y. Liu and Y. M. Chen
Mathematics of Computation
Vol. 51, No. 184 (Oct., 1988), pp. 477-489
DOI: 10.2307/2008759
Stable URL: http://www.jstor.org/stable/2008759
Page Count: 13
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Convergence of a Generalized Pulse-Spectrum Technique (GPST) for Inverse Problems of 1-D Diffusion Equations in Space-Time Domain
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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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