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Abstract:

The Projected Aggregation Methods generate the new point xk+1 as the projection ofxk onto an "aggregate" hyperplane usually arising from linear combinations of the hyperplanes planes defined by the blocks. In [13] an acceleration scheme was introduced for algorithms in which an optimized search direction arises from the solution of small quadratic subproblems. In this paper we extend that theory to classical methods like Cimmino's and to the generalized convex combination as defined in [5]. We prove that the resulting new highly parallel, algorithms improve the original convergence rate and present numerical results which show their outstanding computational efficiency. © 2001 Elsevier B.V. All rights reserved.

Registro:

Documento: Artículo
Título:New optimized and accelerated pam methods for solving large non-symmetric linear systems: Theory and practice
Autor:Scolnik, H.; Echebest, N.; Guardarucci, M.T.; Vacchino, M.C.
Filiación:Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Argentina
Departamento de Matemática, Universidad Nacional de La Plata, Buenos Aires, Argentina
Palabras clave:parallel iterative methods; projected aggregation methods; row partition strategies
Año:2001
Volumen:8
Número:C
Página de inicio:457
Página de fin:471
DOI: http://dx.doi.org/10.1016/S1570-579X(01)80027-6
Título revista:Studies in Computational Mathematics
Título revista abreviado:Stud. Comp. Math.
ISSN:1570579X
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1570579X_v8_nC_p457_Scolnik

Referencias:

  • Aharoni, R., Censor, Y., Block-interactive projection methods for parallel computation of solutions to convex feasibility problems (1989) Linear Algebra Appl., 120, pp. 165-175
  • Björck, A., (1996) Numerical Methods for Least Squares Problems, , SIAM, Philadelphia
  • Bramley, R., Sameh, A., Row projection methods for large nonsymmetric linear systems (1992) SIAM J. Sci. Statist. Comput., 13, pp. 168-193
  • Censor, Y., Zenios, S., (1997) Parallel Optimizations: Theory and Applications, , Oxford University Press, New York
  • Censor, Y., Gordon, D., Gordon, R., Component Averaging: An Efficient Iterative Parallell Algorithms for Large and Sparce Unstructured problems (1988) Technical Report, , (accepted for publication in Parallel Computing), Department of Mathematics, University of Haifa, Israel, November
  • Cimmino, G., Calcolo approssimato per le soluzioni dei sistemi di equazioni lineari (1938) Ric. Sci., 16, pp. 326-333
  • García-Palomares, U.M., Projected aggregation methods for solving a linear system of equalities and inequalities (1991) Akademie-Verlag 62, Berlin, pp. 61-75. , Mathematical Research, Parametric Programming and Related Topics II
  • García-Palomares, U.M., Parallel projected aggreagation 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
  • Kaczmarz, S., Angenäherte Auflösung von Systemen linearer Gleichungen (1937) Bull. Intern. Acad. Polonaise Sci. Lett., 35, pp. 355-357
  • Saad, Y., Schultz, M., Conjugate, gradient-like algorithms for solving nonsymmetric linear systems (1985) Math. Co., 44, pp. 417-424
  • Scolnik, H.D., New Algorithms for Solving Large Sparse Systems of Linear Equations and their Application to Nonlinear Optimization (1997) Investigación Operativa, 7, pp. 103-116
  • Scolnik, H.D., Echebest, N., Guardarucci, M.T., Vacchino, M.C., A New Method for Solving Large Sparse Systems of Linear Equations using row Projections (1998) Proceedings of IMACS Interantional Multiconference Congress Computational Engineering in Systems Applications, pp. 26-30. , Nabuel-Hammamet, Tunisia
  • Scolnik, H.D., Echebest, N., Guardarucci, M.T., Vacchino, M.C., A class of optimized row projection, methods for solving large non-symmetric linear systems (2000) Report Notas de Matemática-74, , (submmited to Applied Numerical Mathematics), Department of Mathematics, University of La Plata, AR

Citas:

---------- APA ----------
Scolnik, H., Echebest, N., Guardarucci, M.T. & Vacchino, M.C. (2001) . New optimized and accelerated pam methods for solving large non-symmetric linear systems: Theory and practice. Studies in Computational Mathematics, 8(C), 457-471.
http://dx.doi.org/10.1016/S1570-579X(01)80027-6
---------- CHICAGO ----------
Scolnik, H., Echebest, N., Guardarucci, M.T., Vacchino, M.C. "New optimized and accelerated pam methods for solving large non-symmetric linear systems: Theory and practice" . Studies in Computational Mathematics 8, no. C (2001) : 457-471.
http://dx.doi.org/10.1016/S1570-579X(01)80027-6
---------- MLA ----------
Scolnik, H., Echebest, N., Guardarucci, M.T., Vacchino, M.C. "New optimized and accelerated pam methods for solving large non-symmetric linear systems: Theory and practice" . Studies in Computational Mathematics, vol. 8, no. C, 2001, pp. 457-471.
http://dx.doi.org/10.1016/S1570-579X(01)80027-6
---------- VANCOUVER ----------
Scolnik, H., Echebest, N., Guardarucci, M.T., Vacchino, M.C. New optimized and accelerated pam methods for solving large non-symmetric linear systems: Theory and practice. Stud. Comp. Math. 2001;8(C):457-471.
http://dx.doi.org/10.1016/S1570-579X(01)80027-6