Mémoire de Maîtrise
DOI
https://doi.org/10.11606/D.11.1979.tde-20231122-100234
Document
Auteur
Nom complet
Agostinho Roberto de Abreu
Unité de l'USP
Domain de Connaissance
Date de Soutenance
Editeur
Piracicaba, 1979
Directeur

Titre en portugais
Estudo estatístico da precisão e do tempo de processamento de vários métodos de resolução de sistemas lineares por computador
Mots-clés en portugais
ANÁLISE ESTATÍSTICA
SISTEMAS LINEARES
Resumé en portugais

Titre en anglais
Not available
Resumé en anglais
This study was carried out with the objective of determining the methods of calculating the solution of linear systems with regard to both time taken for processing and the precision, that is the difference between the exact result and that found by using the method this difference was calculated as the average percentual error. Several of the most common methods used were: 1. Gauss-Jordans method with maximum pivot strategy; 2. Gauss-Jordans method; 3. Choleskys method; 4. Gauss-Seidels method; 5. Jacobis method; 6. Method of Conjugate Gradient. Since some methods require certain types of matrices to calculate the systems, 4 of those were used: 1. Symetric matrix with diagonal dominance; 2. Symetric Matrix without diagonal dominance; 3. Non-symetric matrix with diagonal dominance; 4. Non-symetric matrix without diagonal dominance. Within each type of those matrices, as well as for each method which solves each one of them four repetitions of each order were used. The orders were divided into 2 groups: a 3 to 30 order group and a 31 to 50 one, because the maximum pivot strategy method is too slow to process high orders when this method was used for processing, systems were submitted until the 30th order. The same tendencies were found with order methods, either in the first or in the second group, which means that those most evident method in the first group were also in the second group, for instance, Cholesky Method, which has been show one of the most effective in all categories. Preciseness was found to show itself satisfactory enough for all of those methods which resolved the presented systems, although statistic tests had showed differences among the methods. During processing times of each method striking difference among them were found in the several types of matrices. In this study graphs either for precision or for processing time were used the tendencies of each method may be found for each type of matrix.

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Date de Publication
2023-11-24

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