Geodesic
On Newton-like methods to enclose solutions of nonlinear equations
Applications of Mathematics, Tome 34 (1989) no. 1, pp. 67-84
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We present a class of Newton-like methods to enclose solutions of systems of nonlinear equations. Theorems are derived concerning the feasibility of the method, its global convergence, its speed and the quality of enclosure.
We present a class of Newton-like methods to enclose solutions of systems of nonlinear equations. Theorems are derived concerning the feasibility of the method, its global convergence, its speed and the quality of enclosure.
DOI : 10.21136/AM.1989.104335
Classification : 65G10, 65G30, 65H10
Keywords: interval analysis; Jacobi splitting; enclosure of solutions; interval Jacobian matrix; Newton-like methods; global convergence; numerical examples; Gauss-Seidel splitting; nonlinear equations 
@article{10_21136_AM_1989_104335,
     author = {Mayer, G\"unter},
     title = {On {Newton-like} methods to enclose solutions of nonlinear equations},
     journal = {Applications of Mathematics},
     pages = {67--84},
     year = {1989},
     volume = {34},
     number = {1},
     doi = {10.21136/AM.1989.104335},
     mrnumber = {0982344},
     zbl = {0669.65039},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1989.104335/}
}
TY  - JOUR
AU  - Mayer, Günter
TI  - On Newton-like methods to enclose solutions of nonlinear equations
JO  - Applications of Mathematics
PY  - 1989
SP  - 67
EP  - 84
VL  - 34
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1989.104335/
DO  - 10.21136/AM.1989.104335
LA  - en
ID  - 10_21136_AM_1989_104335
ER  - 
%0 Journal Article
%A Mayer, Günter
%T On Newton-like methods to enclose solutions of nonlinear equations
%J Applications of Mathematics
%D 1989
%P 67-84
%V 34
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1989.104335/
%R 10.21136/AM.1989.104335
%G en
%F 10_21136_AM_1989_104335
Mayer, Günter. On Newton-like methods to enclose solutions of nonlinear equations. Applications of Mathematics, Tome 34 (1989) no. 1, pp. 67-84. doi: 10.21136/AM.1989.104335

[1] G. Alefeld: On the convergence of some interval-arithmetic modifications of Newton's method. SIAM J. Numer. Anal. 21 (1984), 363-372. | DOI | MR | Zbl

[2] G. Alefeld J. Herzberger: Introduction to interval computations. Academic Press, New York, 1983. | MR

[3] C. T. H. Baker: The numerical treatment of integral equations. Clarendon Press, Oxford, 1977. | MR | Zbl

[4] W. Barth. E. Nuding: Optimale Lösung von Intervallgleichungssystemen. Computing 12 (1974), 117-125. | DOI | MR | Zbl

[5] S. Chandrasekhar: Radiative Transfer. Dover, New York, 1960. | MR

[6] P. Frank R. Mises: Die Differential- und Integralgleichungen der Mechanik und Physik. Bd. 1. Nachdruck. Dover Publications, New York, 1961.

[7] A. Frommer: Monotonie und Einschliessung beim Brown-Verfahren. Dissertation, Universisität Karlsruhe, 1986. | Zbl

[8] D. Greenspan: Discrete Numerical Methods in Physics and Engineering. Academic Press, New York, 1974. | MR | Zbl

[9] U. Kulisch W. L. Miranker: Computer Arithmetic in Theory and Practice. Academic Press, New York, 1981. | MR

[10] U. Kulisch W. L. Miranker: A new approach to scientific computation. Academic Press, New York, 1983. | MR

[11] G. Mayer: Comparison theorems for iterative methods based on strong splittings. SIAM J. Numer. Anal. 24 (1987), 215-227. | DOI | MR | Zbl

[12] G. Mayer: Reguläre Zerlegungen und der Satz von Stein und Rosenberg für Intervallmatrizen. Habilitationsschrift. Universität Karlsruhe, 1986.

[13] A. Neumaier: New techniques for the analysis of linear interval equations. Lin. Alg. Appl. 58 (1984), 273-325. | DOI | MR | Zbl

[14] A. Neumaier: Interval iteration for zeros of systems of equations. BIT 25 (1985), 256 - 273. | DOI | MR | Zbl

[15] J. M. Ortega: Numerical analysis. A second course. Academic Press, New York, 1972. | MR | Zbl

[16] J. M. Ortega W. C. Rheinboldt: Iterative solution of nonlinear equations in several variables. Academic Press, New York, 1970. | MR

[17] L. B. Rall: Computational solution of nonlinear operator equations. Krieger Publishing Company, New York, 1979. | MR | Zbl

[18] L. B. Rall: An introduction to the scientific computing language PASCAL-SC. MRC Technical Summary Report # 2644, Mathematics Research Center University of Wisconsin, Madison, 1984.

[19] H. Schwandt: Schnelle fast global konvergente Verfahren für die Fünf-Punkt-Diskretisierung der Poissongleichung mit Dirichletschen Randbedingungen auf Rechteckgebieten. Dissertation, Technische Universität Berlin, 1981. | Zbl

Cité par Sources :