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 | References | Similar Articles | Additional Information

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.

**[1]**J. B. DIAZ & F. T. METCALF, "On iteration procedures for equations of the first kind, , and Picard's criterion for the existence of a solution,"*Math. Comp.*, v. 24, 1970, pp. 923-935. MR**43**#7094. MR**0281376 (43:7094)****[2]**D. K. FADDEEV & V. N. FADDEEVA,*Computational Methods of Linear Algebra*, Fizmatgiz, Moscow, 1960; English transl., Freeman, San Francisco, Calif., 1963. MR**28**#1742; #4659. MR**0158519 (28:1742)****[3]**V. M. FRIDMAN, "Method of successive approximations for a Fredholm integral equation of the first kind,"*Uspehi Mat. Nauk*, v. 11, 1956, no. 1 (67), pp. 233-234. (Russian) MR**17**, 861. MR**0076183 (17:861a)****[4]**A. E. TAYLOR,*Introduction to Functional Analysis*, Wiley, New York; Chapman & Hall, London, 1958. MR**20**#5411. MR**0098966 (20:5411)****[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