References
- Gragg , W. B. and Tapia , R. A. 1974 . Optimal error bounds for the Newton-Kantorovich theorem . SIAM J. Numer. Anal , 11 ( 1 ) : 10 – 13 .
- Hau Bler , W. M. 1986 . A Kantorovich-type convergence analysis for the Gauss-Newton-method . Numer. Math. , 48 ( 1 ) : 119 – 125 .
- Jarratt , P. 1966 . Some fourth order multipoint iterative methods for solving equations . Math. Comp. , 20 ( 1 ) : 434 – 437 .
- Kantorovich , L. 1939 . The method of successive approximations for functional equations . Dokl. Akad. Nauk SSSR , 59 : 1237 – 1240 .
- Kantorovich , L. 1951 . The majorant principle and Newton's method . Dokl. Akad. Nauk SSSR , 80 : 849 – 852 .
- Kantorovich , L. and Akilov , G. “ Fizmatgiz, Moscow ” . In Functional Analysis in Normed Spaces , Pergamon Press . Transl. D. Brown A. Robertson
- Kung , H. T. and Traub , J. F. 1974 . Optimal order of one-point and multipoint iteration . J. ACM , 21 ( 4 ) : 643 – 651 .
- Miel , G. J. 1979 . The Kantorovich theorem with optimal error bounds . Amer. Math. Monthly , 86 : 212 – 215 .
- Miel , G. J. 1980 . Majorizing sequences and error bounds for iterative methods . Math. Comput. , 34 : 185 – 202 .
- Ortega , J. 1968 . The Newton-Kantorovich theorem . Amer. Math. Monthly , 75
- Ortega , J. M. and Rheinboldt , W. C. 1970 . Iterative Solution of Nonlinear Equations in Several Variables , New York : Academe Press .
- Ostrowski , A. 1936 . Konvergenzdiskussion und Fehlerabschatzung fur die Newton'sche methode bei gleichungssystemen, Comment . Math. Helv. , 9 : 79 – 103 .
- Ostrowski , A. 1973 . Solution of Equations and Systems of Equations , New York, London : Academic Press .
- Potra , F. A. 1980 . Sharp error bounds for Newton's process . Numer. Math. , 34 : 63 – 72 .
- Rall , L. 1969 . Computational Solution of Nonlinear Operator Equations , New York : Wiley .
- Traub , J. F. 1964 . Iterative Methods for the Solution of Equations , New York : Prentice-Hall .
- Yamamoto , T. 1985 . Error bounds for Newton's process derived from the Kantovorich theorem . Japan J. Appl. Math. , 2
- Yamamoto , T. 1986 . A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions . Numer. Math. , 49 : 203 – 220 .
- Yamamoto , T. 1987 . A convergence theorem for Newton-like methods in Banach spaces . Numer. Math. , 51 : 545 – 557 .
- Ypma , T. J. 1982 . Affine invariant convergence results for Newton's method . BIT , 22 : 108 – 118 .