An accelerated iterative method with diagonally scaled oblique projections for solving linear feasibility problems
The Projected Aggregation Methods (PAM) for solving linear systems of equalities and/or inequalities, generate a new iterate x k+1 by projecting the current point x k onto a separating hyperplane generated by a given linear combination of the original hyperplanes or halfspaces. In Scolnik et al. (20...
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2005
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02545330_v138_n1_p235_Echebest http://hdl.handle.net/20.500.12110/paper_02545330_v138_n1_p235_Echebest |
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paper:paper_02545330_v138_n1_p235_Echebest2023-06-08T15:21:59Z An accelerated iterative method with diagonally scaled oblique projections for solving linear feasibility problems Exact projection Incomplete projections Oblique projections Projected aggregation methods The Projected Aggregation Methods (PAM) for solving linear systems of equalities and/or inequalities, generate a new iterate x k+1 by projecting the current point x k onto a separating hyperplane generated by a given linear combination of the original hyperplanes or halfspaces. In Scolnik et al. (2001, 2002a) and Echebest et al. (2004) acceleration schemes for solving systems of linear equations and inequalities respectively were introduced, within a PAM like framework. In this paper we apply those schemes in an algorithm based on oblique projections reflecting the sparsity of the matrix of the linear system to be solved. We present the corresponding theoretical convergence results which are a generalization of those given in Echebest et al. (2004). We also present the numerical results obtained applying the new scheme to two algorithms introduced by Garcí a-Palomares and González-Castaño (1998) and also the comparison of its efficiency with that of Censor and Elfving (2002). © 2005 Springer Science + Business Media, Inc. 2005 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02545330_v138_n1_p235_Echebest http://hdl.handle.net/20.500.12110/paper_02545330_v138_n1_p235_Echebest |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Exact projection Incomplete projections Oblique projections Projected aggregation methods |
| spellingShingle |
Exact projection Incomplete projections Oblique projections Projected aggregation methods An accelerated iterative method with diagonally scaled oblique projections for solving linear feasibility problems |
| topic_facet |
Exact projection Incomplete projections Oblique projections Projected aggregation methods |
| description |
The Projected Aggregation Methods (PAM) for solving linear systems of equalities and/or inequalities, generate a new iterate x k+1 by projecting the current point x k onto a separating hyperplane generated by a given linear combination of the original hyperplanes or halfspaces. In Scolnik et al. (2001, 2002a) and Echebest et al. (2004) acceleration schemes for solving systems of linear equations and inequalities respectively were introduced, within a PAM like framework. In this paper we apply those schemes in an algorithm based on oblique projections reflecting the sparsity of the matrix of the linear system to be solved. We present the corresponding theoretical convergence results which are a generalization of those given in Echebest et al. (2004). We also present the numerical results obtained applying the new scheme to two algorithms introduced by Garcí a-Palomares and González-Castaño (1998) and also the comparison of its efficiency with that of Censor and Elfving (2002). © 2005 Springer Science + Business Media, Inc. |
| title |
An accelerated iterative method with diagonally scaled oblique projections for solving linear feasibility problems |
| title_short |
An accelerated iterative method with diagonally scaled oblique projections for solving linear feasibility problems |
| title_full |
An accelerated iterative method with diagonally scaled oblique projections for solving linear feasibility problems |
| title_fullStr |
An accelerated iterative method with diagonally scaled oblique projections for solving linear feasibility problems |
| title_full_unstemmed |
An accelerated iterative method with diagonally scaled oblique projections for solving linear feasibility problems |
| title_sort |
accelerated iterative method with diagonally scaled oblique projections for solving linear feasibility problems |
| publishDate |
2005 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02545330_v138_n1_p235_Echebest http://hdl.handle.net/20.500.12110/paper_02545330_v138_n1_p235_Echebest |
| _version_ |
1768546206889279488 |