New optimized and accelerated pam methods for solving large non-symmetric linear systems: Theory and practice

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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 s...

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Detalles Bibliográficos
Autor principal: Scolnik, H.
Otros Autores: Echebest, N., Guardarucci, M.T, Vacchino, M.C
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: 2001
Acceso en línea:Registro en Scopus
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Biblioteca Central Dr. Luis F. Leloir (FCEN) de Universidad de Buenos Aires
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100 1 |a Scolnik, H. 
245 1 0 |a New optimized and accelerated pam methods for solving large non-symmetric linear systems: Theory and practice 
260 |c 2001 
270 1 0 |m Scolnik, H.; Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos AiresArgentina 
506 |2 openaire  |e Política editorial 
504 |a 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 
504 |a Björck, A., (1996) Numerical Methods for Least Squares Problems, , SIAM, Philadelphia 
504 |a Bramley, R., Sameh, A., Row projection methods for large nonsymmetric linear systems (1992) SIAM J. Sci. Statist. Comput., 13, pp. 168-193 
504 |a Censor, Y., Zenios, S., (1997) Parallel Optimizations: Theory and Applications, , Oxford University Press, New York 
504 |a 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 
504 |a Cimmino, G., Calcolo approssimato per le soluzioni dei sistemi di equazioni lineari (1938) Ric. Sci., 16, pp. 326-333 
504 |a 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 
504 |a García-Palomares, U.M., Parallel projected aggreagation methods for solving the convex feasibility problem (1993) SIAM J. Optim., 3, pp. 882-900 
504 |a 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 
504 |a Kaczmarz, S., Angenäherte Auflösung von Systemen linearer Gleichungen (1937) Bull. Intern. Acad. Polonaise Sci. Lett., 35, pp. 355-357 
504 |a Saad, Y., Schultz, M., Conjugate, gradient-like algorithms for solving nonsymmetric linear systems (1985) Math. Co., 44, pp. 417-424 
504 |a 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 
504 |a 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 
504 |a 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 
520 3 |a 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.  |l eng 
593 |a Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Argentina 
593 |a Departamento de Matemática, Universidad Nacional de La Plata, Buenos Aires, Argentina 
690 1 0 |a PARALLEL ITERATIVE METHODS 
690 1 0 |a PROJECTED AGGREGATION METHODS 
690 1 0 |a ROW PARTITION STRATEGIES 
700 1 |a Echebest, N. 
700 1 |a Guardarucci, M.T. 
700 1 |a Vacchino, M.C. 
773 0 |d 2001  |g v. 8  |h pp. 457-471  |k n. C  |p Stud. Comp. Math.  |x 1570579X  |t Studies in Computational Mathematics 
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856 4 0 |u https://doi.org/10.1016/S1570-579X(01)80027-6  |y DOI 
856 4 0 |u https://hdl.handle.net/20.500.12110/paper_1570579X_v8_nC_p457_Scolnik  |y Handle 
856 4 0 |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1570579X_v8_nC_p457_Scolnik  |y Registro en la Biblioteca Digital 
961 |a paper_1570579X_v8_nC_p457_Scolnik  |b paper  |c PE 
962 |a info:eu-repo/semantics/article  |a info:ar-repo/semantics/artículo  |b info:eu-repo/semantics/publishedVersion 
999 |c 62811 

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