Clenshaw's Method for Evaluating Certain Finite Series | Zendy

D. B. Hunter | Zendy

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Clenshaw's Method for Evaluating Certain Finite Series

Author(s) -

D. B. Hunter

Publication year - 1970

Publication title -

the computer journal

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.319

H-Index - 64

eISSN - 1460-2067

pISSN - 0010-4620

DOI - 10.1093/comjnl/13.4.378

Subject(s) - series (stratigraphy) , recurrence relation , mathematics , quadratic equation , function (biology) , division (mathematics) , relation (database) , derivative (finance) , order (exchange) , algorithm , computer science , calculus (dental) , mathematical analysis , arithmetic , finance , geometry , data mining , medicine , paleontology , dentistry , evolutionary biology , economics , biology

It is shown that Clenshaw's method for evaluating finite series involving functions which satisfy a certain second-order recurrence-relation may be interpreted as a generalisation of the 'synthetic division' method for evaluating polynomials. The process is then extended to give algorithms for dividing by a quadratic factor, and for evaluating the derivative of the series. Methods for obtaining zeros of the function defined by the series are also discussed. (Received October 1969) 1. Summation of finite series Clenshaw (1955) has described a method for evaluating a finite series = 2 1 = 0 (1) in which the functions ,•(*) satisfy a second-order recurrence-relation of the form

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