| Title:
|
An imperfect conjugate gradient algorithm (English) |
| Author:
|
Sloboda, Fridrich |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
27 |
| Issue:
|
6 |
| Year:
|
1982 |
| Pages:
|
426-432 |
| Summary lang:
|
English |
| Summary lang:
|
Slovak |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
A new biorthogonalization algorithm is defined which does not depend on the step-size used. The algorithm is suggested so as to minimize the total error after $n$ steps if imperfect steps are used. The majority of conjugate gradient algorithms are sensitive to the exactness of the line searches and this phenomenon may destroy the global efficiency of these algorithms. (English) |
| Keyword:
|
imperfect conjugate gradient algorithm |
| Keyword:
|
symmetric, positive definite matrix |
| Keyword:
|
biorthogonalization |
| Keyword:
|
line searches |
| Keyword:
|
global efficiency |
| MSC:
|
65F10 |
| MSC:
|
65K05 |
| MSC:
|
90C25 |
| idZBL:
|
Zbl 0503.65017 |
| idMR:
|
MR0678112 |
| DOI:
|
10.21136/AM.1982.103989 |
| . |
| Date available:
|
2008-05-20T18:20:28Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103989 |
| . |
| Reference:
|
[1] M. R. Hestenes E. Stiefel: The method of conjugate gradients for solving linear systems.J. Res. Nat. Bur. Standards, 49 (1952), 409-436. MR 0060307, 10.6028/jres.049.044 |
| Reference:
|
[2] R. Fletcher C. M. Reeves: Function minimization by conjugate gradients.Соmр. J., 2 (1964), 149-154. MR 0187375 |
| Reference:
|
[3] E. Polak G. Ribiere: Note sur le Convergence des Methods de Directions Conjuges.Reone Fr. Int. Rech. Oper. 16R1 (1969), 35-43. MR 0255025 |
| Reference:
|
[4] J. W. Daniel: The conjugate gradient method for linear and nonlinear operator equations.SIAM J. Numer. Anal. 4 (1967), 10-26. Zbl 0154.40302, MR 0217987, 10.1137/0704002 |
| Reference:
|
[5] L. C. W. Dixon: Conjugate Gradient algorithms: Quadratic termination properties without line searches.J. of Inst. of Math. and Applics, 15 (1975), 9-18. MR 0368429, 10.1093/imamat/15.1.9 |
| Reference:
|
[6] L. Nazareth: A conjugate direction algorithm without line searches.JOTA, 3 (1977), 373 - 387. Zbl 0348.65061, MR 0525743, 10.1007/BF00933447 |
| Reference:
|
[7] M. J. Best: A Method to Accelerate the Rate of Convergence of a Class of Optimization Algorithms.Math. Programming, 9 (1975) 139-160. Zbl 0352.90053, MR 0405840, 10.1007/BF01681341 |
| Reference:
|
[8] J. Stoer: On the Relation between Quadratic Termination and Convergence Properties of Minimization Algorithms, Part I. Theory.Num. Math., 28 (1977) 343 - 366. Zbl 0366.65027, MR 0496670 |
| Reference:
|
[9] P. Baptist J. Stoer: On the Relation between Quadratic Termination and Convergence Properties of Minimization Algorithms, Part II, Applications.Num. Math.,28 (1977), 367-391 MR 0496671 |
| . |
