Padé Table - History

History

Although earlier mathematicians had obtained sporadic results involving sequences of rational approximations to transcendental functions, Frobenius (in 1881) was apparently the first to organize the approximants in the form of a table. Henri Padé further expanded this notion in his doctoral thesis Sur la representation approchee d'une fonction par des fractions rationelles, in 1892. Over the ensuing 16 years Padé published 28 additional papers exploring the properties of his table, and relating the table to analytic continued fractions.

Modern interest in Padé tables was revived by H. S. Wall and Oskar Perron, who were primarily interested in the connections between the tables and certain classes of continued fractions. Daniel Shanks and Peter Wynn published influential papers about 1955, and W. B. Gragg obtained far-reaching convergence results during the '70s. More recently, the widespread use of electronic computers has stimulated a great deal of additional interest in the subject.

Read more about this topic:  Padé Table

Famous quotes containing the word history:

    The history of work has been, in part, the history of the worker’s body. Production depended on what the body could accomplish with strength and skill. Techniques that improve output have been driven by a general desire to decrease the pain of labor as well as by employers’ intentions to escape dependency upon that knowledge which only the sentient laboring body could provide.
    Shoshana Zuboff (b. 1951)

    Throughout the history of commercial life nobody has ever quite liked the commission man. His function is too vague, his presence always seems one too many, his profit looks too easy, and even when you admit that he has a necessary function, you feel that this function is, as it were, a personification of something that in an ethical society would not need to exist. If people could deal with one another honestly, they would not need agents.
    Raymond Chandler (1888–1959)

    The whole history of civilisation is strewn with creeds and institutions which were invaluable at first, and deadly afterwards.
    Walter Bagehot (1826–1877)