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On existence criteria and approximation procedures for integral equations of the first kind


Author: C. W. Groetsch
Journal: Math. Comp. 29 (1975), 1105-1108
MSC: Primary 45L05; Secondary 65R05, 47A50
DOI: https://doi.org/10.1090/S0025-5718-1975-0412757-8
MathSciNet review: 0412757
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Abstract: The existence of solutions of Fredholm integral equations of the first kind is characterized in terms of the convergence properties of a general approximation procedure based on a spectral analysis of the integral operator. Applications are given to some iterative and regularization methods. In particular, some results of Diaz and Metcalf are generalized.


References [Enhancements On Off] (What's this?)

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  • [5] A. N. TIHONOV, "Regularization of incorrectly posed problems," Dokl. Akad. Nauk SSSR, v. 153, 1963, pp. 49-52 = Soviet Math. Dokl., v. 4, 1963, pp. 1624-1627. MR 28 #5577. MR 0162378 (28:5577)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1975-0412757-8
Keywords: Integral equations of first kind, compact operator, existence criteria, iterative procedures, regularization
Article copyright: © Copyright 1975 American Mathematical Society

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