A parallel projection method for linear algebraic systems

Fridrich Sloboda

Aplikace matematiky (1978)

  • Volume: 23, Issue: 3, page 185-198
  • ISSN: 0862-7940

Abstract

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A direct projection method for solving systems of linear algebraic equations is described. The algorithm is equivalent to the algorithm for minimization of the corresponding quadratic function and can be generalized for the minimization of a strictly convex function.

How to cite

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Sloboda, Fridrich. "A parallel projection method for linear algebraic systems." Aplikace matematiky 23.3 (1978): 185-198. <http://eudml.org/doc/15049>.

@article{Sloboda1978,
abstract = {A direct projection method for solving systems of linear algebraic equations is described. The algorithm is equivalent to the algorithm for minimization of the corresponding quadratic function and can be generalized for the minimization of a strictly convex function.},
author = {Sloboda, Fridrich},
journal = {Aplikace matematiky},
keywords = {projection method; linear algebraic equations; elimination; orthogonalization; conjugate direction methodds; nonlinear equations; iterative methods for linear systems; Projection Method; Linear Algebraic Equations; Elimination; Orthogonalization; Conjugate Direction Methodds; Nonlinear Equations; Iterative Methods for Linear Systems},
language = {eng},
number = {3},
pages = {185-198},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A parallel projection method for linear algebraic systems},
url = {http://eudml.org/doc/15049},
volume = {23},
year = {1978},
}

TY - JOUR
AU - Sloboda, Fridrich
TI - A parallel projection method for linear algebraic systems
JO - Aplikace matematiky
PY - 1978
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 23
IS - 3
SP - 185
EP - 198
AB - A direct projection method for solving systems of linear algebraic equations is described. The algorithm is equivalent to the algorithm for minimization of the corresponding quadratic function and can be generalized for the minimization of a strictly convex function.
LA - eng
KW - projection method; linear algebraic equations; elimination; orthogonalization; conjugate direction methodds; nonlinear equations; iterative methods for linear systems; Projection Method; Linear Algebraic Equations; Elimination; Orthogonalization; Conjugate Direction Methodds; Nonlinear Equations; Iterative Methods for Linear Systems
UR - http://eudml.org/doc/15049
ER -

References

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  1. R. P. Brent, Algorithms for minimization without derivatives, Prentice-Hall, Englewood Cliffs, New Jersey, (1973). (1973) Zbl0245.65032MR0339493
  2. D. Chazan W. L. Miranker, A nongradient and parallel algorithm for unconstrained minimization, SIAM J. Control, 2 (1970), 207-217. (1970) MR0275637
  3. E. Durand, Solution numérique des equations algebraiques II, Masson, Paris, (1961). (1961) 
  4. D. K. Faddeev V. N. Faddeeva, Computational methods of linear algebra, Fizmatgiz, Moscow, (1960), (Russian). (1960) 
  5. L. Fox H. D. Huskey J. D. Wilkinson, 10.1093/qjmam/1.1.149, Quart. J. Mech. Appl. Math., 1 (1948), 149-173. (1948) MR0026421DOI10.1093/qjmam/1.1.149
  6. N. Gastinel, Analyse numérique linéaire, Hermann, Paris, (1966). (1966) Zbl0151.21202MR0201053
  7. D. Goldfarb, Modification methods for inverting matrices and solving systems of linear algebraic equations, Math. of Соmр., 26 (1972), 829-852. (1972) Zbl0268.65026MR0317527
  8. M. R. Hestenes E. Stiefel, 10.6028/jres.049.044, J. Res. Nat. Bur. Standards, 49 (1952), 409-436. (1952) MR0060307DOI10.6028/jres.049.044
  9. A. S. Householder F. L. Bauer, 10.1007/BF01386209, Numer. Math., 2 (1960), 55-59. (1960) MR0116464DOI10.1007/BF01386209
  10. S. Kaczmarz, Angenäherte Auflösung von Systemen linearen Gleichungen, Bull. Acad. Polon. Sciences et Lettres, A, (1937), 355-357. (1937) 
  11. J. Morris, 10.1080/14786444608561331, Philos. Mag., 37 (1946), 106-120. (1946) Zbl0061.27101MR0018423DOI10.1080/14786444608561331
  12. M. J. D. Powell, An efficient method for finding minimum of a function of several variables without calculating derivatives, Соmр. J., 7 (1964), 155 -162. (1964) MR0187376
  13. E. W. Purcell, The vector method for solving simultaneous linear equations, J. Math. and Phys., 32 (1954), 180-183. (1954) MR0059065
  14. F. Sloboda, Parallel method of conjugate directions for minimization, Apl. mat., 20 (1975), 436-446. (1975) Zbl0326.90050MR0395830
  15. F. Sloboda, Nonlinear iterative methods and parallel computation, Apl. mat., 21 (1976), 252-262. (1976) Zbl0356.65057MR0426411
  16. F. Sloboda, A conjugate directions method and its application, Proc. of the 8th IFIP Conference on Optimization Techniques, Würzburg, (1977), to appear in Springer Verlag. (1977) MR0483450
  17. G. Stewart, 10.1007/BF01436383, Numer. Math., 21 (1973), 285-297. (1973) Zbl0253.65017MR0341837DOI10.1007/BF01436383
  18. P. Václavík, Parallel algorithms for solving 3-diagonal systems of linear equations, (Slovak), Thesis, Fac. of Sc., Komenský Univ., Bratislava (1974). (1974) 

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