Regularization and approximation of linear operator equations in reproducing kernel spaces

Authors:
M. Z. Nashed and Grace Wahba

Journal:
Bull. Amer. Math. Soc. **80** (1974), 1213-1218

MSC (1970):
Primary 47A50, 65J05, 46G22, 65J05, 41A25; Secondary 65D99, 65F20, 45L10

DOI:
https://doi.org/10.1090/S0002-9904-1974-13684-0

MathSciNet review:
0365192

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References | Similar Articles | Additional Information

**1.**N. Aronszajn,*Theory of reproducing kernels*, Trans. Amer. Math. Soc. 68 (1950), 337-404. MR 14, 479. MR**51437****2.**M. Golomb and H. F. Weinberger,*Optimal approximation and error bounds*, On Numerical Approximation (R. E. Langer, editor), Univ. of Wisconsin Press, Madison, Wis., 1959, pp. 117-190. MR**121970****3.**M. M. Lavrent ev,*Some improperly posed problems of mathematical physics*, Izdat. Sibirsk. Otdel. Akad. Nauk SSSR. Novosibirsk, 1962; English transl., Springer Tracts in Natural Philosophy, vol. 11, Springer-Verlag, Berlin, 1967. MR 36 #5487; #7363. MR**224319****4.**M. Z. Nashed,*Generalized inverses, normal solvability, and iteration for singular operator equations*, Nonlinear Functional Analysis and Applications (Proc. Advanced Sem. Math. Res. Center, Univ. of Wisconsin, Madison, Wis., 1970), Academic Press, New York, 1971, pp. 311-359. MR 43 #1003. MR**275246****5.**M. Z. Nashed ,*Some aspects of regularization and approximation of solutions of illposed operator equations*, Proc. Army Numerical Analysis Conference, 1972, pp. 163-181.**6.**M. Z. Nashed and Grace Wahba,*Generalized inverses in reproducing kernel spaces: An approach to regularization of linear operator equations*, SIAM J. Math. Anal. (to appear). MR**358405****7.**M. Z. Nashed and Grace Wahba,*Approximate regularized pseudosolutions of linear operator equations when the data-vector is not in the range of the operator*, (to appear).**8.**M. Z. Nashed and Grace Wahba,*Rates of convergence and approximate least squares solutions of linear integral and operator equations*, Math. Comp. 28 (1974), 69-80. MR**461895****9.**A. N. Tihonov,*On methods of solving incorrect problems*, Proc. Internat. Congress Math. (Moscow, 1966), "Mir", Moscow, 1968, pp. 720-722; English transl., Amer. Math. Soc. Transl. (2) 70 (1968), 222-224. MR 38 #6208. MR**237931****10.**Grace Wahba,*A class of approximate solutions to linear operator equations*, J. Approximation Theory 9 (1973), 61-77. MR**386284**

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DOI:
https://doi.org/10.1090/S0002-9904-1974-13684-0