References
- Dieudonné , J. 1969 . Foundations of Modern Analysis , New York : Academic Press .
- Eiger , A. , Sikorski , K. and Stenger , F. 1984 . A bisection method for systems of nonlinear equations . ACM Trans. Math. Software , 10 : 367 – 377 .
- Gorn , S. 1954 . Maximal convergence intervals and a Gibb's-type phenomenon for Newton's approximation procedure . Ann. Math. , 59 : 463 – 476 .
- Grapsa , T. N. and Vrahatis , M. N. 1989 . The implicit function theorem for solving systems of nonlinear equations in R 2 . Inter. J. Computer Math. , 28 : 171 – 181 .
- Kearfott , R. B. 1979 . An efficient degree-computation method for a generalized method of bisection . Numer. Math. , 32 : 109 – 127 .
- Kearfott , R. B. 1987 . Some tests of generalized bisection . ACM Trans. Math. Software , 13 : 197 – 220 .
- Moré , J. J. 1972 . Nonlinear generalizations of matrix diagonal dominance with application to Gauss-Seidel iterations . SIAM J. Numer. Anal. , 9 : 357 – 378 .
- Moré , J. J. , Garbow , B. S. and Hillstrom , K. E. 1981 . Testing unconstrained optimization software . ACM Trans. Math. Software , 7 : 17 – 41 .
- Ortega , J. M. 1972 . Numerical Analysis , New York : Academic Press .
- Ortega , J. M. and Rheinboldt , W. C. 1970 . “ Numerical Solution of Nonlinear Problems ” . In Local and Global Convergence of Generalized Linear Iterations , Edited by: Ortega , J. M. and Rheinboldt , W. C. 122 – 143 . SIAM .
- Ortega , J. M. and Rheinboldt , W. C. 1970 . Iterative Solution of Nonlinear Equations in Several Variables , New York : Academic Press .
- Ortega , J. M. and Rockoff , M. 1966 . Nonlinear difference equations and Gauss-Seidel type iterative methods . SIAM J. Numer. Anal. , 3 : 497 – 513 .
- Ostrowski , A. 1973 . Solution of Equations in Euclidean and Banach Spaces , London : Academic Press .
- Rheinboldt , W. C. 1974 . Methods for Solving Systems of Equations , Philadelphia : SIAM .
- Sikorski , K. 1982 . Bisection is optimal . Numer. Math. , 40 : 111 – 117 .
- Traub , J. F. 1964 . Iterative Methods for the Solution of Equations , Englewood Cliffs, , NJ : Prentice-Hall, Inc. .
- Vrahatis M. N. The topological degree for the generalized method of bisection Dept. of Mathematics, Univ. of Patras Patras, Greece 1981 Tech. Rep. #6
- Vrahatis , M. N. 1986 . An error estimation for the method of bisection in n . Bull. Greek Math. Soc. , 27 : 161 – 174 .
- Vrahatis , M. N. 1988 . Solving systems of nonlinear equations using the nonzero value of the topological degree . ACM Trans. Math. Software , 14 : 312 – 329 .
- Vrahatis , M. N. 1988 . CHABIS: A mathematical software package for locating and evaluating roots of systems of nonlinear equations . ACM Trans. Math. Software , 14 : 330 – 336 .
- Vrahatis , M. N. and Bountis , T. C. A convergence-improving iterative method for computing periodic orbits near bifurcation points . J. Comp. Phys. , to appear
- Vrahatis , M. N. and Iordanidis , K. I. 1986 . A rapid generalized method of bisection for solving systems of non-linear equations . Numer. Math. , 49 : 123 – 138 .
- Yamamoto , N. 1984 . Regularization of solutions of nonlinear equations with singular Jacobian matrices . J. Infor. Processing , 7 : 16 – 21 .
- Weber , H. and Werner , W. 1981 . On the accurate determination of nonisolated solutions of nonlinear equations . Computing , 26 : 315 – 326 .