An imperfect conjugate gradient algorithm

Fridrich Sloboda

Aplikace matematiky (1982)

  • Volume: 27, Issue: 6, page 426-432
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Sloboda, Fridrich. "An imperfect conjugate gradient algorithm." Aplikace matematiky 27.6 (1982): 426-432. <http://eudml.org/doc/15263>.

@article{Sloboda1982,
abstract = {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.},
author = {Sloboda, Fridrich},
journal = {Aplikace matematiky},
keywords = {imperfect conjugate gradient algorithm; symmetric; positive definite matrix; biorthogonalization; line searches; global efficiency; imperfect conjugate gradient algorithm; symmetric, positive definite matrix; biorthogonalization; line searches; global efficiency},
language = {eng},
number = {6},
pages = {426-432},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An imperfect conjugate gradient algorithm},
url = {http://eudml.org/doc/15263},
volume = {27},
year = {1982},
}

TY - JOUR
AU - Sloboda, Fridrich
TI - An imperfect conjugate gradient algorithm
JO - Aplikace matematiky
PY - 1982
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 27
IS - 6
SP - 426
EP - 432
AB - 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.
LA - eng
KW - imperfect conjugate gradient algorithm; symmetric; positive definite matrix; biorthogonalization; line searches; global efficiency; imperfect conjugate gradient algorithm; symmetric, positive definite matrix; biorthogonalization; line searches; global efficiency
UR - http://eudml.org/doc/15263
ER -

References

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  2. R. Fletcher C. M. Reeves, Function minimization by conjugate gradients, Соmр. J., 2 (1964), 149-154. (1964) Zbl0132.11701MR0187375
  3. E. Polak G. Ribiere, Note sur le Convergence des Methods de Directions Conjuges, Reone Fr. Int. Rech. Oper. 16R1 (1969), 35-43. (1969) Zbl0174.48001MR0255025
  4. J. W. Daniel, 10.1137/0704002, SIAM J. Numer. Anal. 4 (1967), 10-26. (1967) Zbl0154.40302MR0217987DOI10.1137/0704002
  5. L. C. W. Dixon, 10.1093/imamat/15.1.9, J. of Inst. of Math. and Applics, 15 (1975), 9-18. (1975) Zbl0294.90076MR0368429DOI10.1093/imamat/15.1.9
  6. L. Nazareth, 10.1007/BF00933447, JOTA, 3 (1977), 373 - 387. (1977) Zbl0348.65061MR0525743DOI10.1007/BF00933447
  7. M. J. Best, 10.1007/BF01681341, Math. Programming, 9 (1975) 139-160. (1975) Zbl0352.90053MR0405840DOI10.1007/BF01681341
  8. J. Stoer, On the Relation between Quadratic Termination and Convergence Properties of Minimization Algorithms, Part I. Theory, Num. Math., 28 (1977) 343 - 366. (1977) Zbl0366.65027MR0496670
  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 (1977) Zbl0366.65028MR0496671

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