Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



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
Full-text PDF

References | Similar Articles | Additional Information

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

  • 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

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1970): 47A50, 65J05, 46G22, 65J05, 41A25, 65D99, 65F20, 45L10

Retrieve articles in all journals with MSC (1970): 47A50, 65J05, 46G22, 65J05, 41A25, 65D99, 65F20, 45L10

Additional Information


American Mathematical Society