| Title:
|
A parallel projection method for linear algebraic systems (English) |
| Author:
|
Sloboda, Fridrich |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
23 |
| Issue:
|
3 |
| Year:
|
1978 |
| Pages:
|
185-198 |
| Summary lang:
|
English |
| Summary lang:
|
Slovak |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
projection method |
| Keyword:
|
linear algebraic equations |
| Keyword:
|
elimination |
| Keyword:
|
orthogonalization |
| Keyword:
|
conjugate direction methodds |
| Keyword:
|
nonlinear equations |
| Keyword:
|
iterative methods for linear systems |
| MSC:
|
65F10 |
| MSC:
|
65F20 |
| MSC:
|
65F25 |
| MSC:
|
65H10 |
| MSC:
|
93C99 |
| idZBL:
|
Zbl 0398.65013 |
| idMR:
|
MR0490260 |
| DOI:
|
10.21136/AM.1978.103744 |
| . |
| Date available:
|
2008-05-20T18:09:27Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103744 |
| . |
| Reference:
|
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| Reference:
|
[2] D. Chazan W. L. Miranker: A nongradient and parallel algorithm for unconstrained minimization.SIAM J. Control, 2 (1970), 207-217. MR 0275637 |
| Reference:
|
[3] E. Durand: Solution numérique des equations algebraiques II.Masson, Paris, (1961). |
| Reference:
|
[4] D. K. Faddeev V. N. Faddeeva: Computational methods of linear algebra.Fizmatgiz, Moscow, (1960), (Russian). |
| Reference:
|
[5] L. Fox H. D. Huskey J. D. Wilkinson: Notes on the solution of algebraic linear simutaneous equations.Quart. J. Mech. Appl. Math., 1 (1948), 149-173. MR 0026421, 10.1093/qjmam/1.1.149 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[8] 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:
|
[9] A. S. Householder F. L. Bauer: On certain iterative methods for solving linear systems.Numer. Math., 2 (1960), 55-59. MR 0116464, 10.1007/BF01386209 |
| Reference:
|
[10] S. Kaczmarz: Angenäherte Auflösung von Systemen linearen Gleichungen.Bull. Acad. Polon. Sciences et Lettres, A, (1937), 355-357. |
| Reference:
|
[11] J. Morris: An escalator process for the solution of linear simultaneous equations.Philos. Mag., 37 (1946), 106-120. Zbl 0061.27101, MR 0018423, 10.1080/14786444608561331 |
| Reference:
|
[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. MR 0187376 |
| Reference:
|
[13] E. W. Purcell: The vector method for solving simultaneous linear equations.J. Math. and Phys., 32 (1954), 180-183. MR 0059065, 10.1002/sapm1953321180 |
| Reference:
|
[14] F. Sloboda: Parallel method of conjugate directions for minimization.Apl. mat., 20 (1975), 436-446. Zbl 0326.90050, MR 0395830 |
| Reference:
|
[15] F. Sloboda: Nonlinear iterative methods and parallel computation.Apl. mat., 21 (1976), 252-262. Zbl 0356.65057, MR 0426411 |
| Reference:
|
[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. MR 0483450 |
| Reference:
|
[17] G. Stewart: Conjugate direction methods for solving systems of linear equations.Numer. Math., 21 (1973), 285-297. Zbl 0253.65017, MR 0341837, 10.1007/BF01436383 |
| Reference:
|
[18] P. Václavík: Parallel algorithms for solving 3-diagonal systems of linear equations.(Slovak), Thesis, Fac. of Sc., Komenský Univ., Bratislava (1974). |
| . |
