Accession Number:

AD0723555

Title:

A New Approach to Evaluation of Infinite Processes,

Descriptive Note:

Corporate Author:

NAVAL ORDNANCE LAB WHITE OAK MD

Personal Author(s):

Report Date:

1971-03-01

Pagination or Media Count:

89.0

Abstract:

The simplest forms of discrete infinite processes, such as infinite series, products, continued fractions and their generalizations are considered. It is shown that by associating such processes with equivalent linear difference equations with boundary conditions at infinity a means of classifying them in a unified way is provided, as well as a means of evaluating asymptotic approximations to remainder sequences. If the approximate remainder sequences are introduced at the definitional level, so that the value of the infinite process is defined as a limit of successive stages of the finite process with an approximate remainder term included at each stage, two benefits result. First, where the process converges by the Cauchy definition zero remainder terms, convergence is speeded, so that numerical computations of value are aided. Secondly, where the process is Cauchy-divergent, it may nevertheless be summed to a useful value. A broad class of processes, termed asymptotically tractable, is identified for which these benefits are obtained. Author

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE