# A parallel projection method for linear algebraic systems

Aplikace matematiky (1978)

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

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topSloboda, 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

top- R. P. Brent, Algorithms for minimization without derivatives, Prentice-Hall, Englewood Cliffs, New Jersey, (1973). (1973) Zbl0245.65032MR0339493
- D. Chazan W. L. Miranker, A nongradient and parallel algorithm for unconstrained minimization, SIAM J. Control, 2 (1970), 207-217. (1970) Zbl0223.65022MR0275637
- E. Durand, Solution numérique des equations algebraiques II, Masson, Paris, (1961). (1961)
- D. K. Faddeev V. N. Faddeeva, Computational methods of linear algebra, Fizmatgiz, Moscow, (1960), (Russian). (1960) Zbl0094.11005
- L. Fox H. D. Huskey J. D. Wilkinson, 10.1093/qjmam/1.1.149, Quart. J. Mech. Appl. Math., 1 (1948), 149-173. (1948) Zbl0033.28503MR0026421DOI10.1093/qjmam/1.1.149
- N. Gastinel, Analyse numérique linéaire, Hermann, Paris, (1966). (1966) Zbl0151.21202MR0201053
- D. Goldfarb, Modification methods for inverting matrices and solving systems of linear algebraic equations, Math. of Соmр., 26 (1972), 829-852. (1972) Zbl0268.65026MR0317527
- M. R. Hestenes E. Stiefel, 10.6028/jres.049.044, J. Res. Nat. Bur. Standards, 49 (1952), 409-436. (1952) Zbl0048.09901MR0060307DOI10.6028/jres.049.044
- A. S. Householder F. L. Bauer, 10.1007/BF01386209, Numer. Math., 2 (1960), 55-59. (1960) Zbl0168.13501MR0116464DOI10.1007/BF01386209
- S. Kaczmarz, Angenäherte Auflösung von Systemen linearen Gleichungen, Bull. Acad. Polon. Sciences et Lettres, A, (1937), 355-357. (1937) Zbl0017.31703
- J. Morris, 10.1080/14786444608561331, Philos. Mag., 37 (1946), 106-120. (1946) Zbl0061.27101MR0018423DOI10.1080/14786444608561331
- 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) Zbl0132.11702MR0187376
- E. W. Purcell, The vector method for solving simultaneous linear equations, J. Math. and Phys., 32 (1954), 180-183. (1954) MR0059065
- F. Sloboda, Parallel method of conjugate directions for minimization, Apl. mat., 20 (1975), 436-446. (1975) Zbl0326.90050MR0395830
- F. Sloboda, Nonlinear iterative methods and parallel computation, Apl. mat., 21 (1976), 252-262. (1976) Zbl0356.65057MR0426411
- 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) Zbl0372.90106MR0483450
- G. Stewart, 10.1007/BF01436383, Numer. Math., 21 (1973), 285-297. (1973) Zbl0253.65017MR0341837DOI10.1007/BF01436383
- 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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