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

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**0051437**, 10.1090/S0002-9947-1950-0051437-7**2.**Michael Golomb and Hans F. Weinberger,*Optimal approximation and error bounds*, On numerical approximation. Proceedings of a Symposium, Madison, April 21–23, 1958, Edited by R. E. Langer. Publication No. 1 of the Mathematics Research Center, U.S. Army, the University of Wisconsin, The University of Wisconsin Press, Madison, Wis., 1959, pp. 117–190. MR**0121970****3.**M. M. Lavrent′ev,*O nekotorykh nekorrektnykh zadachakh matematicheskoi fiziki*, Izdat. Sibirsk. Otdel. Akad. Nauk SSSR, Novosibirsk, 1962 (Russian). MR**0224319****4.**M. Z. Nashed,*Generalized inverses, normal solvability, and iteration for singular operator equations*, Nonlinear Functional Anal. and Appl. (Proc. Advanced Sem., Math. Res. Center, Univ. of Wisconsin, Madison, Wis., 1970) Academic Press, New York, 1971, pp. 311–359. MR**0275246****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.**5**(1974), 974–987. MR**0358405****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,*Convergence rates of approximate least squares solutions of linear integral and operator equations of the first kind*, Math. Comp.**28**(1974), 69–80. MR**0461895**, 10.1090/S0025-5718-1974-0461895-1**9.**A. N. Tihonov,*On methods of solving incorrectly formulated problems*, Proc. Internat. Congr. Math. (Moscow, 1966) Izdat. “Mir”, Moscow, 1968, pp. 720–722 (Russian). MR**0237931****10.**Grace Wahba,*A class of approximate solutions to linear operator equations*, J. Approximation Theory**9**(1973), 61–77. MR**0386284**

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