Artículo
Echebest, N.; Guardarucci, M.T.; Scolnik, H.; Vacchino, M.C. "An acceleration scheme for solving convex feasibility problems using incomplete projection algorithms" (2004) Numerical Algorithms. 35(2-4):331-350
Estamos trabajando para incorporar este artículo al repositorio
Consulte la política de Acceso Abierto del editor
Abstract:
The Projected Aggregation Methods (PAM) for solving linear systems of equalities and/or inequalities, generate a new iterate xk+1 by projecting the current point xk onto a separating hyperplane generated by a given linear combination of the original hyperplanes or half-spaces. In [12] we introduced acceleration schemes for solving systems of linear equations by applying optimization techniques to the problem of finding the optimal combination of the hyperplanes within a PAM like framework. In this paper we generalize those results, introducing a new accelerated iterative method for solving systems of linear inequalities, together with the corresponding theoretical convergence results. In order to test its efficiency, numerical results obtained applying the new acceleration scheme to two algorithms introduced by García-Palomares and González- Castaño [6] are given.
Registro:
| Documento: | Artículo |
| Título: | An acceleration scheme for solving convex feasibility problems using incomplete projection algorithms |
| Autor: | Echebest, N.; Guardarucci, M.T.; Scolnik, H.; Vacchino, M.C. |
| Filiación: | Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, Argentina Departamento de Computación, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Argentina |
| Palabras clave: | Aggregated projection methods; Incomplete projections; Systems of inequalities |
| Año: | 2004 |
| Volumen: | 35 |
| Número: | 2-4 |
| Página de inicio: | 331 |
| Página de fin: | 350 |
| DOI: | http://dx.doi.org/10.1023/B:NUMA.0000021777.31773.c3 |
| Título revista: | Numerical Algorithms |
| Título revista abreviado: | Numer. Algorithms |
| ISSN: | 10171398 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10171398_v35_n2-4_p331_Echebest |
Referencias:
- 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., (1997) Parallel Optimization: Theory and Applications, , Oxford Univ. 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
- García-Palomares, U.M., González-Castaño, F.J., Incomplete projection algorithms for solving the convex feasibility problem (1998) Numer. Algorithms, 18, pp. 177-193
- 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
- Herman, G.T., Meyer, L.B., Algebraic reconstruction techniques can be made computationally efficient (1993) IEEE Trans. Medical Imaging, 12, pp. 600-609
- Saad, Y., SPARSKIT: A basic tool kit for sparse matrix computations (1990) Technical Report 90-20, , Research Institute for Avanced Computer Science. NASA Ames Research Center, Moffet Field, CA
- 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 (2002) Appl. Numer. Math., 41 (4), pp. 499-513
- Scolnik, H.D., Echebest, N., Guardarucci, M.T., Vacchino, M.C., Acceleration scheme for parallel projected aggregation methods for solving large linear systems (2002) Ann. Oper. Res., 117 (1-4), pp. 95-115
- Scolnik, H.D., Echebest, N., Guardarucci, M.T., Vacchino, M.C., New optimized and accelerated PAM methods for solving large non-symmetric linear systems: Theory and practice (2001) Inherently Parallel Algorithms in Feasibility and Optimization and their Applications, 8. , eds. D. Butnariu, Y. Censor and S. Reich, Studies in Computational Mathematics (Elsevier Science, Amsterdam
Citas:
---------- APA ----------
Echebest, N., Guardarucci, M.T., Scolnik, H. & Vacchino, M.C. (2004) . An acceleration scheme for solving convex feasibility problems using incomplete projection algorithms. Numerical Algorithms, 35(2-4), 331-350.http://dx.doi.org/10.1023/B:NUMA.0000021777.31773.c3
---------- CHICAGO ----------
Echebest, N., Guardarucci, M.T., Scolnik, H., Vacchino, M.C. "An acceleration scheme for solving convex feasibility problems using incomplete projection algorithms" . Numerical Algorithms 35, no. 2-4 (2004) : 331-350.http://dx.doi.org/10.1023/B:NUMA.0000021777.31773.c3
---------- MLA ----------
Echebest, N., Guardarucci, M.T., Scolnik, H., Vacchino, M.C. "An acceleration scheme for solving convex feasibility problems using incomplete projection algorithms" . Numerical Algorithms, vol. 35, no. 2-4, 2004, pp. 331-350.http://dx.doi.org/10.1023/B:NUMA.0000021777.31773.c3
---------- VANCOUVER ----------
Echebest, N., Guardarucci, M.T., Scolnik, H., Vacchino, M.C. An acceleration scheme for solving convex feasibility problems using incomplete projection algorithms. Numer. Algorithms. 2004;35(2-4):331-350.http://dx.doi.org/10.1023/B:NUMA.0000021777.31773.c3
