Navegar

Colección

Datos Estadísticas

Artículo

La versión final de este artículo es de uso interno de la institución.
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

The optimal and the accelerated row projection methods for solving large nonsymmetric linear systems were discussed. These algorithms use a partition strategy into blocks based on sequential estimations of their condition numbers. These algorithms are extremely fast and efficient, but they do not converge always. A block splitting algorithm which fulfills the conditions based on the sequential estimations of the condition numbers was also discussed. The performance of the projection methods was highly dependent on the way in which the rows of the matrix were split into blocks.

Registro:

Documento: Artículo
Título:A class of optimized row projection methods for solving large nonsymmetric linear systems
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, Buenos Aires, Argentina
Departamento de Matemática, Universidad de la Plata, Buenos Aires, Argentina
Palabras clave:Parallel iterative methods; Projected aggregate methods; Row partition strategies; Convergence of numerical methods; Heuristic methods; Linear systems; Matrix algebra; Optimization; Parallel algorithms; Partial differential equations; Quadratic programming; Vectors; Projected aggregate methods (PAM); Row partition strategies; Iterative methods
Año:2002
Volumen:41
Número:4
Página de inicio:499
Página de fin:513
DOI: http://dx.doi.org/10.1016/S0168-9274(01)00131-3
Título revista:Applied Numerical Mathematics
Título revista abreviado:Appl Numer Math
ISSN:01689274
CODEN:ANMAE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01689274_v41_n4_p499_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
  • Björck, A., (1996) Numerical Methods for Least Squares Problems, , SIAM, Philadelphia, PA
  • Bramley, R., Sameh, A., Row projection methods for large nonsymmetric linear systems (1992) SIAM J. Sci. Statist. Comput., 13, pp. 168-193
  • Censor, Y., Parallel application of block-iterative methods in medical imaging and radiation therapy (1988) Math. Programming, 42, pp. 307-325
  • Censor, Y., Zenios, S.A., (1997) Parallel Optimization: Theory, Algorithms, and Applications, , Oxford University Press, New York
  • Cimmino, G., Calcolo approssimato per le soluzioni dei sistemi di equazioni lineari (1938) Ricerca Sci. II, 9, pp. 326-333
  • Fletcher, R., (1987) Practical Methods of Optimization, 2nd edn., , Wiley, New York
  • García-Palomares, U.M., Projected aggregation methods for solving a linear system of equalities and inequalities (1991) Mathematical Research, 62, pp. 61-75. , J. Guddat, H.Th. Jongen, B. Kummer, F. Nozicka (Eds.), Parametric Optimization and Related Topics II, Akademie Verlag, Berlin
  • 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. Math. Phys., 7, pp. 1-24
  • Householder, A.S., Bauer, F.L., On certain iterative methods for solving linear systems (1960) Numer. Math., 2, pp. 55-59
  • Kaczmarz, S., Angenäherte auflösung von systemen linearer gleichungen (1937) Bull. Internat. Acad. Polonaise Sci. Lett., 35, pp. 355-357
  • Saad, Y., Schultz, M.H., Conjugate gradient-like algorithms for solving nonsymmetric linear systems (1985) Math. Comp., 44, pp. 417-424
  • Saad, Y., (1990) SPARSKIT: A basic tool kit for sparse matrix computations, , Technical Report 90-20, Research Institute for Advanced Computer Science, NASA Ames Research Center, Moffett Field, CA
  • 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 class of optimized row projection methods for solving large nonsymmetric linear systems (2000) Notas de Matemática, 74. , Technical Report, Department of Mathematics, University of La Plata, Buenos Aires, Argentina
  • Van der Vorst, H., A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems (1992) SIAM J. Sci. Statist. Comput., 13, pp. 631-644

Citas:

---------- APA ----------
Scolnik, H., Echebest, N., Guardarucci, M.T. & Vacchino, M.C. (2002) . A class of optimized row projection methods for solving large nonsymmetric linear systems. Applied Numerical Mathematics, 41(4), 499-513.
http://dx.doi.org/10.1016/S0168-9274(01)00131-3
---------- CHICAGO ----------
Scolnik, H., Echebest, N., Guardarucci, M.T., Vacchino, M.C. "A class of optimized row projection methods for solving large nonsymmetric linear systems" . Applied Numerical Mathematics 41, no. 4 (2002) : 499-513.
http://dx.doi.org/10.1016/S0168-9274(01)00131-3
---------- MLA ----------
Scolnik, H., Echebest, N., Guardarucci, M.T., Vacchino, M.C. "A class of optimized row projection methods for solving large nonsymmetric linear systems" . Applied Numerical Mathematics, vol. 41, no. 4, 2002, pp. 499-513.
http://dx.doi.org/10.1016/S0168-9274(01)00131-3
---------- VANCOUVER ----------
Scolnik, H., Echebest, N., Guardarucci, M.T., Vacchino, M.C. A class of optimized row projection methods for solving large nonsymmetric linear systems. Appl Numer Math. 2002;41(4):499-513.
http://dx.doi.org/10.1016/S0168-9274(01)00131-3