Numerical solving of equations in the work of José Mariano Vallejo |
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Authors: | José-Miguel Pacheco Castelao F Javier Pérez-Fernández Carlos-Oswaldo Suárez Alemán |
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Institution: | (1) Departamento de Matemáticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira, 35017 Las Palmas de Gran Canaria, Spain;(2) Departamento de Matemáticas, Universidad de Cádiz, P. Box 40, 11510 Puerto Real (Cádiz), Spain |
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Abstract: | The progress of Mathematics during the nineteenth century was characterised both by an enormous acquisition of new knowledge
and by the attempts to introduce rigour in reasoning patterns and mathematical writing. Cauchy’s presentation of Mathematical
Analysis was not immediately accepted, and many writers, though aware of that new style, did not use it in their own mathematical
production. This paper is devoted to an episode of this sort that took place in Spain during the first half of the century:
It deals with the presentation of a method for numerically solving algebraic equations by José Mariano Vallejo, a late Spanish
follower of the Enlightenment ideas, politician, writer, and mathematician who published it in the fourth (1840) edition of
his book Compendio de Matemáticas Puras y Mistas, claiming to have discovered it on his own. Vallejo’s main achievement was to write down the whole procedure in a very careful
way taking into account the different types of roots, although he paid little attention to questions such as convergence checks
and the fulfilment of the hypotheses of Rolle’s Theorem. For sure this lack of mathematical care prevented Vallejo to occupy
a place among the forerunners of Computational Algebra. |
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