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

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 and F. T. Metcalf,*On iteration procedures for equations of the first kind, 𝐴𝑥=𝑦, and Picard’s criterion for the existence of a solution*, Math. Comp.**24**(1970), 923–935. MR**0281376**, 10.1090/S0025-5718-1970-0281376-4**[2]**D. K. Faddeev and V. N. Faddeeva,*Computational methods of linear algebra*, Translated by Robert C. Williams, W. H. Freeman and Co., San Francisco-London, 1963. MR**0158519****[3]**V. M. Fridman,*Method of successive approximations for a Fredholm integral equation of the 1st kind*, Uspehi Mat. Nauk (N.S.)**11**(1956), no. 1(67), 233–234 (Russian). MR**0076183****[4]**Angus E. Taylor,*Introduction to functional analysis*, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1958. MR**0098966****[5]**A. N. Tihonov,*On the regularization of ill-posed problems*, Dokl. Akad. Nauk SSSR**153**(1963), 49–52 (Russian). MR**0162378**

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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