Literature cited
A. Ben-Israel, “A modified Newton-Raphson method for the solution of systems of equations,” Israel J. Math.,3, No. 1, 94–98 (1965).
A. Ben-Israel, “A Newton-Raphson method for the solution of systems of equations,” J. Math. Analysis and Applications,15, 243–253 (1966).
L. Aleksandrov, “A regularized iterative process for the solution of nonlinear operator equations,” Preprint JINR, R5-5137, Dubna, 3–13 (1970).
V. N. Kublanovskaya, “On an approach to the solution of the inverse eigenvalue problem,” Seminars in Mathematics, Vol. 18, Consultants Bureau, New York (1972), pp. 80–86.
L. S. Jennings and M. R. Osborne, “Applications of orthogonal matrix transformations to the solution of systems of linear and nonlinear equations,” The Australian National University, Technical report, No. 37, 1–45 (1970).
M. N. Yakovlev, “On certain methods of solution of nonlinear equations,” Tr. Matem. In-ta Akad. Nauk SSSR, No. 84, 8–39 (1965).
G. Golub, “Numerical methods for solving linear least squares problems,” Numer. Math.,7, No. 3, 206–216 (1965).
D. K. Faddeev, V. N. Kublanovskaya, and V. N. Faddeeva, “Linear algebraic systems with rectangular matrices,” in: Modern Numerical Methods, No. 1, Computational Methods of Linear Algebra (Proc. Internat. Summer School on Numerical Methods, Kiev, 1966).
V. V. Voevodin, “Orthogonal transformations and the solution of systems of equations with rectangular matrices. Round-off errors in algebraic process,” in: Collection of Reports of the Seminar of the Computing Center, Moscow State University [in Russian], Moscow (1968), pp. 39–58.
V. N. Kublanovskaya, “On the calculation of a generalized inverse matrix and projector,” Zh. Vychis. Mat. i Mat. Fiz.,6, No. 2, 326–332 (1966).
L. V. Kantorovich, “Newton's method,” Tr. Matem. Inst. Steklov,28, 104–144 (1949).
Additional information
The basic results of this article were presented as a report at the IFIP Congress in 1971.
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 23, pp. 53–71, 1971.
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Kublanovskaya, V.N. The application of orthogonal transformations to the solution of nonlinear systems. J Math Sci 2, 388–404 (1974). https://doi.org/10.1007/BF01098996
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DOI: https://doi.org/10.1007/BF01098996