Literature Cited
A. N. Tikhonov, “On regularization of incorrectly formulated problems,” Dokl. Akad. Nauk SSSR,153, No. 1, 49–52 (1963).
V. K. Ivanov, “Approximate solution of operator equations of the first kind,” Zh. Vychislit. Matem. i Mat. Fiz.,6, No. 6, 1089–1094 (1966).
D. L. Phillips, “A technique for numerical solution of certain integral equations of the first kind,” J. Assoc. Comput. Machinery,119, No. 1, 84–97 (1962).
V. A. Morozov, “On the principle of residuals in solving operator equations by a regularization method,” Zh. Vychislit. Matem. i Mat. Fiz.,8, No. 2, 295–305 (1968).
V. V. Ivanov and V. Yu. Kudrinskii, “Approximate solution of linear operator equations in Hilbert space by the method of least squares,” Zh. Vychislit. Matem. i Mat. Fiz.,16, No. 5, 831–841 (1966).
V. V. Vasin and V. P. Tanana, “Approximate solution of operator equations of the first kind,” Mat. Zap. Ural'sk. Un-ta,6, No. 4, 27–37 (1968).
V. P. Tanana, “Incorrectly formulated problems and geometries of Banach spaces,” Dokl. Akad. Nauk SSSR,193, No. 1, 43–45 (1970).
V. V. Vasin, “On a projection method of approximate solution of incorrectly formulated problems,” Izv. Vyssh. Uchebn. Zaved. Matematika, No. 11, 28–32 (1971).
V. P. Tanana, “Variational methods of solution of operator equations of the first kind,” Mat. Zap. Ural'sk. Un-ta,8, No. 2, 108–129 (1970).
V. A. Morozov, “Convergence of an approximate method of solution of operator equations of the first kind,” Zh. Vychislit. Matem. i Mat. Fiz.,13, No. 1, 3–17 (1973).
A. V. Goncharskii, A. S. Leonov, and A. G. Yagola, “Finite-difference approximation of linear incorrectly formulated problems,” Zh. Vychislit. Matem. i Mat. Fiz.,14, No. 1, 15–24 (1974).
A. V. Goncharskii, A. S. Leonov, and A. G. Yagola, “Generalized principle of residual,” Zh. Vychislit. Matem. i Mat. Fiz.,13, No. 2, 294–302 (1973).
Fan Ky and J. Glicksberg, “Some geometric properties of spheres in a normed linear space,” Duke Math. J.,25, No. 4, 553–568 (1958).
V. L. Klee, “Convexity of Chebyshev sets,” Math. Ann.,142, No. 3, 292–304 (1961).
V. F. Sholokhovich, “On a method of numerical solution of unstable extremal problems,” Izv. Vyssh. Uchebn. Zaved. Matematika, No. 6, 92–100 (1972).
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 16, No. 6, pp. 1301–1307, November–December, 1975.
Rights and permissions
About this article
Cite this article
Tanana, V.P. Projection methods and finite-difference approximation of linear incorrectly formulated problems. Sib Math J 16, 999–1004 (1975). https://doi.org/10.1007/BF00967398
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00967398