| Title:
|
On Brown's method with convexity hypotheses (English) |
| Author:
|
Milaszewicz, Juan Pedro |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
49 |
| Issue:
|
2 |
| Year:
|
2004 |
| Pages:
|
165-184 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Given two initial points generating monotone convergent Brown iterations in the context of the monotone Newton theorem (MNT), it is proved that if one of them is an upper bound of the other, then the same holds for each pair of respective terms in the Brown sequences they generate. This comparison result is carried over to the corresponding Brown-Fourier iterations. An illustration is discussed. (English) |
| Keyword:
|
nonlinear systems |
| Keyword:
|
convex functions |
| Keyword:
|
Brown’s method |
| Keyword:
|
monotone convergence |
| Keyword:
|
Fourier iterates |
| MSC:
|
65H10 |
| idZBL:
|
Zbl 1099.65045 |
| idMR:
|
MR2043080 |
| DOI:
|
10.1023/B:APOM.0000027222.62203.3c |
| . |
| Date available:
|
2009-09-22T18:17:33Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134565 |
| . |
| Reference:
|
[1] R. Brent: Some efficient algorithms for solving systems of nonlinear equations.SIAM J. Numer. Anal. 10 (1973), 327–344. Zbl 0258.65051, MR 0331764, 10.1137/0710031 |
| Reference:
|
[2] K. Brown: A quadratically convergent Newton-like method based upon Gaussian elimination.SIAM J. Numer. Anal. 6 (1969), 560–569. Zbl 0245.65023, MR 0263229, 10.1137/0706051 |
| Reference:
|
[3] A. Frommer: Monotonicity of Brown’s method.Z. Angew. Math. Mech. 68 (1988), 101–109. Zbl 0663.65047, MR 0931771, 10.1002/zamm.19880680211 |
| Reference:
|
[4] A. Frommer: Comparison of Brown’s and Newton’s method in the monotone case.Numer. Math. 52 (1988), 511–521. Zbl 0628.65039, MR 0945097, 10.1007/BF01400889 |
| Reference:
|
[5] J. P. Milaszewicz, S. Abdel Masih: Elimination and fixed point iterations.Comput. Math. Appl. 25 (1993), 43–53. MR 1199911, 10.1016/0898-1221(93)90197-4 |
| Reference:
|
[6] J. P. Milaszewicz: Comparison theorems for monotone Newton-Fourier iterations and applications in functional elimination.Linear Algebra Appl. 220 (1995), 343–357 343–357. Zbl 0844.65050, MR 1334584 |
| Reference:
|
[7] J. P. Milaszewicz: Comparison theorems for a third order method.Appl. Math. Lett. 10 (1997), 17–21. Zbl 0883.65046, MR 1429469, 10.1016/S0893-9659(96)00104-8 |
| Reference:
|
[8] J. P. Milaszewicz: On Brown’s and Newton’s methods with convexity hypotheses.J. Comput. Appl. Math. 150 (2002), 1–24. MR 1946879, 10.1016/S0377-0427(02)00489-2 |
| Reference:
|
[9] J. M. Ortega, W. C. Rheinboldt: Iterative Solution of Nonlinear Equations in Several Variables.Academic Press, New York-London, 1970. MR 0273810 |
| Reference:
|
[10] A. M. Ostrowski: Solution of Equations and Systems of Equations.Academic Press, New York-London, 1960. MR 0216746 |
| Reference:
|
[11] H. Schwetlick: Numerische Lösung Nichtlinearer Gleichungssysteme.R. Oldenburg Verlag, München, 1979. |
| Reference:
|
[12] R. S. Varga: Matrix Iterative Analysis.Prentice-Hall, Englewood Cliffs, 1962. MR 0158502 |
| . |
