Artículo
Scolnik, H.; Echebest, N.; Guardarucci, M.T.; Vacchino, M.C. "Acceleration Scheme for Parallel Projected Aggregation Methods for Solving Large Linear Systems" (2002) Annals of Operations Research. 117(1-4):95-115
Consulte la política de Acceso Abierto del editor
Abstract:
The Projected Aggregation methods generate the new point xk+1 as the projection of xk onto an "aggregate" hyperplane usually arising from linear combinations of the hyperplanes defined by the blocks. The aim of this paper is to improve the speed of convergence of a particular kind of them by projecting the directions given by the blocks onto the aggregate hyperplane defined in the last iteration. For that purpose we apply the scheme introduced in "A new method for solving large sparse systems of linear equations using row projections" [11], for a given block projection algorithm, to some new methods here introduced whose main features are related to the fact that the projections do not need to be accurately computed. Adaptative splitting schemes are applied which take into account the structure and conditioning of the matrix. It is proved that these new highly parallel algorithms improve the original convergence rate and present numerical results which show their computational efficiency.
Registro:
| Documento: | Artículo |
| Título: | Acceleration Scheme for Parallel Projected Aggregation Methods for Solving Large Linear Systems |
| Autor: | Scolnik, H.; Echebest, N.; Guardarucci, M.T.; Vacchino, M.C. |
| Filiación: | Departamento de Computación, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Argentina Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, La Plata, Argentina |
| Palabras clave: | Parallel iterative methods; Projected aggregation methods; Row partition strategies |
| Año: | 2002 |
| Volumen: | 117 |
| Número: | 1-4 |
| Página de inicio: | 95 |
| Página de fin: | 115 |
| DOI: | http://dx.doi.org/10.1023/A:1021565305371 |
| Título revista: | Annals of Operations Research |
| Título revista abreviado: | Ann. Oper. Res. |
| ISSN: | 02545330 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02545330_v117_n1-4_p95_Scolnik |
Referencias:
- Aharoni, R., Censor, Y., Block-iterative projection methods for parallel computation of solutions to convex feasibility problems (1989) Linear Algebra Appl., 120, pp. 165-175
- Bramley, R., Sameh, A., Row projection methods for large nonsymmetric linear systems (1992) SIAM J. Sci. Statist. Comput., 13, pp. 168-193
- Censor, Y., Gordon, D., Gordon, R., (1998) Component Averaging: An Efficient Iterative Parallel Algorithm for Large and Sparce Unstructured Problems, , Technical Report, Department of Mathematics, University of Haifa, Israel (accepted for publication in Parallel Computing)
- Censor, Y., Zenios, S., (1997) Parallel Optimization: Theory and Applications, , Oxford University Press, New York
- Cimmino, G., Calcolo approssimato per le soluzioni dei sistemi di equazioni lineari (1938) Ric. Sci., 16, pp. 326-333
- García-Palomares, U.M., Parallel projected aggregation methods for solving the convex feasibility problem (1993) SIAM J. Optim., 3, pp. 882-900
- Gubin, L.G., Polyak, B.T., Raik, E.V., The method of projections for finding the common point of convex sets (1967) USSR Comput. Math. and Math. Phys., 7, pp. 1-24
- Iusem, A., De Pierro, A., Convergence results for an accelerated nonlinear Cimmino algorithm (1986) Numer. Math., 49, pp. 367-378
- Kaczmarz, S., Angenäherte Auflösung von Systemen linearer Gleichungen (1937) Bull. Intern. Acad. Polonaise Sci. Lett., 35, pp. 355-357
- Scolnik, H.D., A new method for solving large sparse systems of linear equations using row projections (1998) Proceedings of IMACS International Multiconference Congress Computational Engineering in Systems Applications, pp. 26-30. , Nabeul-Hammamet, Tunisia
- Scolnik, H.D., (2000) A Class of Optimized Row Projection Methods for Solving Large Non-Symmetric Linear Systems, Report Notas de Matemática-74, , Department of Mathematics, University of La Plata, to appear in Applied Numerical Mathematics
Citas:
---------- APA ----------
Scolnik, H., Echebest, N., Guardarucci, M.T. & Vacchino, M.C. (2002) . Acceleration Scheme for Parallel Projected Aggregation Methods for Solving Large Linear Systems. Annals of Operations Research, 117(1-4), 95-115.http://dx.doi.org/10.1023/A:1021565305371
---------- CHICAGO ----------
Scolnik, H., Echebest, N., Guardarucci, M.T., Vacchino, M.C. "Acceleration Scheme for Parallel Projected Aggregation Methods for Solving Large Linear Systems" . Annals of Operations Research 117, no. 1-4 (2002) : 95-115.http://dx.doi.org/10.1023/A:1021565305371
---------- MLA ----------
Scolnik, H., Echebest, N., Guardarucci, M.T., Vacchino, M.C. "Acceleration Scheme for Parallel Projected Aggregation Methods for Solving Large Linear Systems" . Annals of Operations Research, vol. 117, no. 1-4, 2002, pp. 95-115.http://dx.doi.org/10.1023/A:1021565305371
---------- VANCOUVER ----------
Scolnik, H., Echebest, N., Guardarucci, M.T., Vacchino, M.C. Acceleration Scheme for Parallel Projected Aggregation Methods for Solving Large Linear Systems. Ann. Oper. Res. 2002;117(1-4):95-115.http://dx.doi.org/10.1023/A:1021565305371
