| Title:
|
On Newton-like methods to enclose solutions of nonlinear equations (English) |
| Author:
|
Mayer, Günter |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
34 |
| Issue:
|
1 |
| Year:
|
1989 |
| Pages:
|
67-84 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
interval analysis |
| Keyword:
|
Jacobi splitting |
| Keyword:
|
enclosure of solutions |
| Keyword:
|
interval Jacobian matrix |
| Keyword:
|
Newton-like methods |
| Keyword:
|
global convergence |
| Keyword:
|
numerical examples |
| Keyword:
|
Gauss-Seidel splitting |
| Keyword:
|
nonlinear equations |
| MSC:
|
65G10 |
| MSC:
|
65G30 |
| MSC:
|
65H10 |
| idZBL:
|
Zbl 0669.65039 |
| idMR:
|
MR0982344 |
| DOI:
|
10.21136/AM.1989.104335 |
| . |
| Date available:
|
2008-05-20T18:36:02Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104335 |
| . |
| Reference:
|
[1] G. Alefeld: On the convergence of some interval-arithmetic modifications of Newton's method.SIAM J. Numer. Anal. 21 (1984), 363-372. Zbl 0536.65026, MR 0736338, 10.1137/0721027 |
| Reference:
|
[2] G. Alefeld J. Herzberger: Introduction to interval computations.Academic Press, New York, 1983. MR 0733988 |
| Reference:
|
[3] C. T. H. Baker: The numerical treatment of integral equations.Clarendon Press, Oxford, 1977. Zbl 0373.65060, MR 0467215 |
| Reference:
|
[4] W. Barth. E. Nuding: Optimale Lösung von Intervallgleichungssystemen.Computing 12 (1974), 117-125. Zbl 0275.65008, MR 0398075, 10.1007/BF02260368 |
| Reference:
|
[5] S. Chandrasekhar: Radiative Transfer.Dover, New York, 1960. MR 0111583 |
| Reference:
|
[6] P. Frank R. Mises: Die Differential- und Integralgleichungen der Mechanik und Physik.Bd. 1. Nachdruck. Dover Publications, New York, 1961. |
| Reference:
|
[7] A. Frommer: Monotonie und Einschliessung beim Brown-Verfahren.Dissertation, Universisität Karlsruhe, 1986. Zbl 0613.65051 |
| Reference:
|
[8] D. Greenspan: Discrete Numerical Methods in Physics and Engineering.Academic Press, New York, 1974. Zbl 0288.65001, MR 0362905 |
| Reference:
|
[9] U. Kulisch W. L. Miranker: Computer Arithmetic in Theory and Practice.Academic Press, New York, 1981. MR 0606741 |
| Reference:
|
[10] U. Kulisch W. L. Miranker: A new approach to scientific computation.Academic Press, New York, 1983. MR 0721972 |
| Reference:
|
[11] G. Mayer: Comparison theorems for iterative methods based on strong splittings.SIAM J. Numer. Anal. 24 (1987), 215-227. Zbl 0614.65030, MR 0874747, 10.1137/0724018 |
| Reference:
|
[12] G. Mayer: Reguläre Zerlegungen und der Satz von Stein und Rosenberg für Intervallmatrizen.Habilitationsschrift. Universität Karlsruhe, 1986. |
| Reference:
|
[13] A. Neumaier: New techniques for the analysis of linear interval equations.Lin. Alg. Appl. 58 (1984), 273-325. Zbl 0558.65019, MR 0739292, 10.1016/0024-3795(84)90217-9 |
| Reference:
|
[14] A. Neumaier: Interval iteration for zeros of systems of equations.BIT 25 (1985), 256 - 273. Zbl 0575.65045, MR 0785818, 10.1007/BF01935003 |
| Reference:
|
[15] J. M. Ortega: Numerical analysis. A second course.Academic Press, New York, 1972. Zbl 0248.65001, MR 0403154 |
| Reference:
|
[16] J. M. Ortega W. C. Rheinboldt: Iterative solution of nonlinear equations in several variables.Academic Press, New York, 1970. MR 0273810 |
| Reference:
|
[17] L. B. Rall: Computational solution of nonlinear operator equations.Krieger Publishing Company, New York, 1979. Zbl 0476.65033, MR 0601777 |
| Reference:
|
[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. |
| Reference:
|
[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 0474.65037 |
| . |
