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This programme is a case study of the problem of calculating logarithms. It concentrates on the numerical methods of functional representation for the function 1n (1+x).
Metadata describing this Open University video programme
Module code and title: M351, Numerical computation
Item code: M351; 05
First transmission date: 23-05-1976
Published: 1976
Rights Statement:
Restrictions on use:
Duration: 00:24:00
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Producer: John Richmond
Contributors: Leslie Fox; Peter Thomas
Publisher: BBC Open University
Keyword(s): Chebyshev polynomials; Logarithms; Remez algorithm
Footage description: Thomas explains that the programme will show to compute the log of a number. Leslie Fox, of Oxford University, briefly describes the advantages of approximation over log tables. With the aid of animation, Fox approximates In(1+x) on [0, 1] by its Taylor series about x=0 and x=0.5 and examines the corresponding error functions. Using the graph-plotter, Thomas indicates the error on the log curve. The plotter then magnifies the error 100 times. A computer animation shows how the error curve alters as the location points are changed, and how to achieve the best possible curve. Thomas uses the graph plotter to explain why the computer-produced curve is the best that can be achieved. Fox uses the Remez Algorithm and the computer terminal to show how to obtain an approximation which minimizes the maximum error and obtain the minimax cubic polynomical to approximate In(1+x). Using computer animation, Thomas shows how the Remez Algorithm operates successfully with poor starting values for x. Fox briefly explains that, if a greater degree of accuracy is required in estimating errors, the Taylor series is inadequate. Thomas explains the Chebyshev polynomicals and shows these have the equioscillation property. He shows that these polynomicals can be transformed from the interval -1,1 to O,l and called Tr. Fox shows how to expand In (1+x) as a Chebyshev series which, when truncated, is approximately a minimax polynomial.
Master spool number: 6HT/72070
Production number: 00525_4224
Videofinder number: 852
Available to public: no