Accession Number:

AD0707617

Title:

FIVE LECTURES ON THE NUMERICAL APPLICATION OF CONTINUED FRACTIONS,

Descriptive Note:

Corporate Author:

WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s):

Report Date:

1970-01-01

Pagination or Media Count:

181.0

Abstract:

In the first lecture the structure of the continued fraction is described and various ways of deriving continued fractions are discussed. The second lecture deals with a mechanism of convergence which includes the greater number of known continued fraction expansions. The third and fourth lectures are concerned with those continued fractions which both for direct application in the calculation of functions and for their use in the acceleration of slowly convergent iterative processes are of by far the greatest importance, namely continued fractions which are derived by the transformation of power series. The fifth lecture describes a number of formal procedures for transforming power series into continued fractions. It is shown how one of these methods may be used as the basis of a powerful technique for accelerating the convergence of iterative processes.

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE