An extension of the I + Smax preconditioner for the Gauss-Seidel method
A preconditioning technique based on the application of a fixed but arbitrary number of I + Smax steps is proposed. A reduction of the spectral radius of the Gauss-Seidel iteration matrix is theoretically analyzed for diagonally dominant Z-matrices. In particular, it is shown that after a finite...
| Main Authors: | , , |
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| Format: | Article |
| Language: | Spanish |
| Published: |
Universidad Industrial de Santander
2013-06-01
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| Series: | Revista Integración |
| Subjects: | |
| Online Access: | http://revistas.uis.edu.co/index.php/revistaintegracion/article/view/3361/3535 |
| _version_ | 1828815158243229696 |
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| author | Isnardo Arenas Paul Castillo Xuerong Yong |
| author_facet | Isnardo Arenas Paul Castillo Xuerong Yong |
| author_sort | Isnardo Arenas |
| collection | DOAJ |
| description | A preconditioning technique based on the application of a fixed
but arbitrary number of I + Smax steps is proposed. A reduction of the spectral
radius of the Gauss-Seidel iteration matrix is theoretically analyzed for
diagonally dominant Z-matrices. In particular, it is shown that after a finite
number of steps this matrix reduces to null matrix. To illustrate the performance
of the proposed technique numerical experiments on a wide variety of
matrices are presented. Point and block versions of the preconditioner are
numerically studied.
Resumen. Se propone una técnica de precondicionamiento para el método de
Gauss-Seidel basada en la aplicación de una cantidad de pasos arbitrarios pero
fijos del precondicionador I +Smax. Se analiza de manera teórica la reducción
del radio espectral de la matriz de iteración del método de Gauss-Seidel para
Z-matrices diagonalmente dominantes. En particular, se demuestra que después
de un número finito de pasos esta matriz se reduce a una matriz nula.
Para ilustrar la eficacia de la técnica propuesta se presentan experimentos
numéricos para una amplia variedad de matrices. Se estudian numéricamente
versiones puntuales y de bloques del precondicionador. |
| first_indexed | 2024-12-12T10:38:04Z |
| format | Article |
| id | doaj.art-41ad4609352943ee9f9bc76e4c9ba996 |
| institution | Directory Open Access Journal |
| issn | 0120-419X 2145-8472 |
| language | Spanish |
| last_indexed | 2024-12-12T10:38:04Z |
| publishDate | 2013-06-01 |
| publisher | Universidad Industrial de Santander |
| record_format | Article |
| series | Revista Integración |
| spelling | doaj.art-41ad4609352943ee9f9bc76e4c9ba9962022-12-22T00:27:07ZspaUniversidad Industrial de SantanderRevista Integración0120-419X2145-84722013-06-01311114An extension of the I + Smax preconditioner for the Gauss-Seidel methodIsnardo Arenas0 Paul Castillo1Xuerong Yong2University of Puerto RicoUniversity of Puerto RicoUniversity of Puerto RicoA preconditioning technique based on the application of a fixed but arbitrary number of I + Smax steps is proposed. A reduction of the spectral radius of the Gauss-Seidel iteration matrix is theoretically analyzed for diagonally dominant Z-matrices. In particular, it is shown that after a finite number of steps this matrix reduces to null matrix. To illustrate the performance of the proposed technique numerical experiments on a wide variety of matrices are presented. Point and block versions of the preconditioner are numerically studied. Resumen. Se propone una técnica de precondicionamiento para el método de Gauss-Seidel basada en la aplicación de una cantidad de pasos arbitrarios pero fijos del precondicionador I +Smax. Se analiza de manera teórica la reducción del radio espectral de la matriz de iteración del método de Gauss-Seidel para Z-matrices diagonalmente dominantes. En particular, se demuestra que después de un número finito de pasos esta matriz se reduce a una matriz nula. Para ilustrar la eficacia de la técnica propuesta se presentan experimentos numéricos para una amplia variedad de matrices. Se estudian numéricamente versiones puntuales y de bloques del precondicionador.http://revistas.uis.edu.co/index.php/revistaintegracion/article/view/3361/3535PreconditioningGauss-Seidel methodregular splittingpoint and block preconditionersPrecondicionamientométodo Gauss-Seideldescomposiciones regularesprecondicionadores de punto y bloque |
| spellingShingle | Isnardo Arenas Paul Castillo Xuerong Yong An extension of the I + Smax preconditioner for the Gauss-Seidel method Revista Integración Preconditioning Gauss-Seidel method regular splitting point and block preconditioners Precondicionamiento método Gauss-Seidel descomposiciones regulares precondicionadores de punto y bloque |
| title | An extension of the I + Smax preconditioner for the Gauss-Seidel method |
| title_full | An extension of the I + Smax preconditioner for the Gauss-Seidel method |
| title_fullStr | An extension of the I + Smax preconditioner for the Gauss-Seidel method |
| title_full_unstemmed | An extension of the I + Smax preconditioner for the Gauss-Seidel method |
| title_short | An extension of the I + Smax preconditioner for the Gauss-Seidel method |
| title_sort | extension of the i smax preconditioner for the gauss seidel method |
| topic | Preconditioning Gauss-Seidel method regular splitting point and block preconditioners Precondicionamiento método Gauss-Seidel descomposiciones regulares precondicionadores de punto y bloque |
| url | http://revistas.uis.edu.co/index.php/revistaintegracion/article/view/3361/3535 |
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