Iterative refinement of the Gauss-Jordan method, in ill conditioned systems.
In this paper, an iterative algorithm is constructed to improve the solution of a system of linear equations, of the form Ax = b, when it is solved using the Gauss-Jordan Method and by using finite arithmetic. Understanding the functioning of the algorithm, showing its scope and analyzing how it is...
| Main Authors: | , |
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| Format: | Online |
| Language: | spa |
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Universidad Pedagógica y Tecnológica de Colombia
2019
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| Online Access: | https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/8761 |
| _version_ | 1801706344327151616 |
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| author | Mesa, Astrid Yesenia Calvache Archila, Alvaro |
| author_facet | Mesa, Astrid Yesenia Calvache Archila, Alvaro |
| author_sort | Mesa, Astrid Yesenia |
| collection | OJS |
| description | In this paper, an iterative algorithm is constructed to improve the solution of a system of linear equations, of the form Ax = b, when it is solved using the Gauss-Jordan Method and by using finite arithmetic. Understanding the functioning of the algorithm, showing its scope and analyzing how it is deduced, is achieved through the concept of matrix norm, together with some of its properties. The concept of the condition number of a matrix is introduced, and are found bounds for it by using the matrix norms. Finally, it is explained the iterative algorithm of the Refinement, showing the power of this one, when it is solved a system of linear equations ill conditioned. |
| format | Online |
| id | oai:oai.revistas.uptc.edu.co:article-8761 |
| institution | Revista Ciencia en Desarrollo |
| language | spa |
| publishDate | 2019 |
| publisher | Universidad Pedagógica y Tecnológica de Colombia |
| record_format | ojs |
| spelling | oai:oai.revistas.uptc.edu.co:article-87612020-11-11T02:06:46Z Iterative refinement of the Gauss-Jordan method, in ill conditioned systems. Refinamiento iterativo del Método de Gauss-Jordan, en sistemas mal condicionados Mesa, Astrid Yesenia Calvache Archila, Alvaro Norma matricial, números de condición, Método de Refinamiento. Matrix norm, condition numbers, Refinement Method. In this paper, an iterative algorithm is constructed to improve the solution of a system of linear equations, of the form Ax = b, when it is solved using the Gauss-Jordan Method and by using finite arithmetic. Understanding the functioning of the algorithm, showing its scope and analyzing how it is deduced, is achieved through the concept of matrix norm, together with some of its properties. The concept of the condition number of a matrix is introduced, and are found bounds for it by using the matrix norms. Finally, it is explained the iterative algorithm of the Refinement, showing the power of this one, when it is solved a system of linear equations ill conditioned. En este Artículo, se construye un algoritmo iterativo para mejorar la solución de un sistema de ecuaciones lineales, de la forma Ax=b, cuando se resuelve utilizando el Método de Gauss-Jordan y utilizando aritmética finita. Comprender el funcionamiento del algoritmo, mostrar su alcance y analizar cómo se dedujo, se logra a través del concepto de norma matricial, junto con algunas de sus propiedades. Se introduce el concepto del número de condición de una matriz, y se le encuentran cotas mediante el uso de las normas matriciales. Finalmente, se expone el algoritmo iterativo del Refinamiento, que muestra el poder de éste, al resolver un sistema de Ecuaciones lineales mal condicionadas. Universidad Pedagógica y Tecnológica de Colombia 2019-07-23 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Text Texto application/pdf https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/8761 10.19053/01217488.v10.n2.2019.8761 Ciencia En Desarrollo; Vol. 10 No. 2 (2019): Vol 10, Núm. 2 (2019): Julio - Diciembre; 113-124 Ciencia en Desarrollo; Vol. 10 Núm. 2 (2019): Vol 10, Núm. 2 (2019): Julio - Diciembre; 113-124 2462-7658 0121-7488 spa https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/8761/8716 |
| spellingShingle | Norma matricial, números de condición, Método de Refinamiento. Matrix norm, condition numbers, Refinement Method. Mesa, Astrid Yesenia Calvache Archila, Alvaro Iterative refinement of the Gauss-Jordan method, in ill conditioned systems. |
| title | Iterative refinement of the Gauss-Jordan method, in ill conditioned systems. |
| title_alt | Refinamiento iterativo del Método de Gauss-Jordan, en sistemas mal condicionados |
| title_full | Iterative refinement of the Gauss-Jordan method, in ill conditioned systems. |
| title_fullStr | Iterative refinement of the Gauss-Jordan method, in ill conditioned systems. |
| title_full_unstemmed | Iterative refinement of the Gauss-Jordan method, in ill conditioned systems. |
| title_short | Iterative refinement of the Gauss-Jordan method, in ill conditioned systems. |
| title_sort | iterative refinement of the gauss jordan method in ill conditioned systems |
| topic | Norma matricial, números de condición, Método de Refinamiento. Matrix norm, condition numbers, Refinement Method. |
| topic_facet | Norma matricial, números de condición, Método de Refinamiento. Matrix norm, condition numbers, Refinement Method. |
| url | https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/8761 |
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