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1: – IntegerInput
On entry: the number of terms in the series (i.e., one greater than the degree of the polynomial).
2: – const doubleInput
On entry: must be set to the value of the th coefficient in the series, for .
3: – doubleInput
On entry: , the argument at which the polynomial is to be evaluated. It should lie in the range to , but a value just outside this range is permitted (see Section 9) to allow for possible rounding errors committed in the transformation from to discussed in Section 3. Provided the recommended form of the transformation is used, a successful exit is thus assured whenever the value of lies in the range to .
4: – double *Output
On exit: the value of the polynomial.
5: – NagError *Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
On entry, , where is the machine precision.
In this case the value of p is set arbitrarily to zero.
The rounding errors committed are such that the computed value of the polynomial is exact for a slightly perturbed set of coefficients . The ratio of the sum of the absolute values of the to the sum of the absolute values of the is less than a small multiple of machine precision.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
e02aec is not threaded in any implementation.
The time taken by e02aec is approximately proportional to .
It is expected that a common use of e02aec will be the evaluation of the polynomial approximations produced by e02adc and e02afc.
Evaluate at 11 equally-spaced points in the interval the polynomial of degree 4 with Chebyshev coefficients, , , , , 0.0625.
The example program is written in a general form that will enable a polynomial of degree in its Chebyshev series form to be evaluated at equally-spaced points in the interval . The program is self-starting in that any number of datasets can be supplied.