| Title:
|
On a method of D. Marsal for equations with positive operators (English) |
| Author:
|
Marek, Ivo |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
15 |
| Issue:
|
6 |
| Year:
|
1970 |
| Pages:
|
413-417 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper is studied the equation $(^*)x=Tx+f$ in a complex Banach space $X$, its ordering being given by a normal reproducing cone $K$. Under the assumption that $(^*)$ has exactly one solution in $K$ it is shown that a certain sequence $(w_p)$ (given by iterations - which is an analogue of Marsal's method) converges to $x^*$. The paper is a generalization of Marsal's results. () |
| MSC:
|
65F10 |
| MSC:
|
65J05 |
| idZBL:
|
Zbl 0274.65019 |
| idMR:
|
MR0283596 |
| DOI:
|
10.21136/AM.1970.103315 |
| . |
| Date available:
|
2008-05-20T17:49:15Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103315 |
| . |
| Reference:
|
[1] M. G. Krein M. A. Rutman: Linear operators leaving invariant a cone in a Banach space.Uspekhi Mat. Nauk III (1948), N 3, 3-95 (Russian). MR 0027128 |
| Reference:
|
[2] I. Marek: Iterations of linear bounded operators in non self-adjoint eigenvalue problems and Kellogg's iterations.Czech. Math. J. 12 (1962), 536-554. MR 0149297 |
| Reference:
|
[3] D. Marsal: Konvergenzbeschleunigte Iteration von linearen Gleichungssystemen bei Divergenz des klassischen Verfahren und besonderer Berücksichtigung von Randwertproblemen.Computing 4 (1969), 234-245. MR 0248972, 10.1007/BF02234772 |
| Reference:
|
[4] H. Schaefer: Halbgeordnete lokalkonvexe Vektorräume.Math. Ann. 135 (1958), 115-141. Zbl 0080.31501, MR 0106401, 10.1007/BF01343098 |
| . |
