On a Suboptimal Filtration Method for Solving Convolution-Type Integral Equations of the First Kind

ISSN： 0022-247X

Source： Journal of Mathematical Analysis and Applications, Vol.226, Iss.2, 1998-10, pp. : 292-308

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Abstract

In this paper a so-called local regularization method (Arsenin et al., USSR Comput. Math. Math. Phys. 28(3) (1988), 113–125; Arsenin and Timinov, Soviet Math. Dokl. 32(2) (1985), 566–570; Tikhonov et al., “Mathematical Problems of Computer Tomography,” Nauka, Moscow, 1987) for solving convolution-type integral equations of the first kind is analyzed. It is shown that to increase the precision of the solution, it is appropriate to do only one approximation in the iterative scheme of this method. It is also shown that this method should not be interpreted as a method with variable regularization parameter α; one should view it as a method of suboptimal filtration. A new variant of a suboptimal filtration method is formulated.