Numerical solving of equations in the work of José Mariano Vallejo

详细信息    查看全文

• 作者：José-Miguel Pacheco Castelao ; F. Javier Pérez-Fernández and Carlos-Oswaldo Suárez Alemán
• 刊名：Archive for History of Exact Sciences
• 出版年：2007
• 出版时间：September, 2007
• 年：2007
• 卷：61
• 期：5
• 页码：537-552
• 全文大小：376 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  History of Mathematics
  Mathematics
  Physics
  Mathematical and Computational Physics
  Astronomy
  Astrophysics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0657

文摘

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.