Resumen 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.

Abstract 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.

Estudou-se em condições controladas, o efeito das temperaturas de 14, 21 e 28°C na germinação de três cultivares de Vigna unguiculata, Phaseolus vulgaris e Glycine max. As sementes foram acondicionadas em placas de Petri com algodão e papel de filtro , mantidos sob alta umidade. Maior germinação foi observada a 21°C em relação as temperaturas de 14 e 28°C, para os cultivares de vigna, feijoeiro e soja. Melhor germinação foi apresentada pelos cultivares de feijoeiro Carioca e Goiano Precoce, seguidos pelo feijoeiro 'Rosinha' , vigna ' EPACE 1' e soja 'Davis' a 21ºC. Os cultivares de vigna, adaptados a altas temperaturas, apresentaram problemas na germinação a 14ºC. Normalmente a velocidade de emergência do hipocólito revelou-se inferior a velocidade de emergência da radícula.

This experiment was carried out to study the effects of the temperatures of 14, 21 and 28°C on germination of three cultivars of Vigna unguiculata, Phaseolus vulgaris and Glycine max. The seeds where germinated on Petri dishes provided with cotton and filter paper, maintained in incubator with high humidity. The Petri dishes were maintained under controlled temperature conditions. Higher germination was observed at 21°C in relation to temperatures of 14 and 28°C, for Vigna, bean and soybean cultivars. Best germination were showed by 'Carioca' and 'Goiano Precoce' beans,followed by 'Rosinha' bean, 'EPACE 1' Vigna and 'Davis' soybean at 21°C. Vigna cultivars adapted to high temperatures presented problems for germination at 14°C. Normaly velocity of hypocotyl emergence was lower tham velocity of radicle emergence.