C06DBF (PDF version)
C06 Chapter Contents
C06 Chapter Introduction
NAG Library Manual

NAG Library Routine Document


Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

C06DBF returns the value of the sum of a Chebyshev series through the routine name.

2  Specification

REAL (KIND=nag_wp) C06DBF
REAL (KIND=nag_wp)  X, C(N)

3  Description

C06DBF evaluates the sum of a Chebyshev series of one of three forms according to the value of the parameter S:
S=1: 0.5 c1 + j=2 n cj T j-1 x , S=2: 0.5 c1 + j=2 n cj T 2j-2 x , S=3: j=1 n cj T 2j-1 x
where x lies in the range -1.0 x 1.0 . Here Tr x  is the Chebyshev polynomial of order r in x, defined by cosry  where cosy=x .
The method used is based upon a three-term recurrence relation; for details see Clenshaw (1962).

4  References

Clenshaw C W (1962) Chebyshev Series for Mathematical Functions Mathematical tables HMSO

5  Parameters

1:     X – REAL (KIND=nag_wp)Input
On entry: the argument x of the series.
Constraint: -1.0 X 1.0.
2:     C(N) – REAL (KIND=nag_wp) arrayInput
On entry: Cj must contain the coefficient cj of the Chebyshev series, for j=1,2,,n.
3:     N – INTEGERInput
On entry: n, the number of terms in the series.
4:     S – INTEGERInput
On entry: must have the value 1, 2 or 3 according to whether the series is general, even or odd respectively (see Section 3). For all other values of S, the routine behaves as though S=2.

6  Error Indicators and Warnings

If an error is detected in an input parameter C06DBF will act as if a soft noisy exit has been requested (see Section 3.3.4 in the Essential Introduction).

7  Accuracy

There may be a loss of significant figures due to cancellation between terms. However, provided that n is not too large, C06DBF yields results which differ little from the best attainable for the available machine precision.

8  Further Comments

The time taken increases with n.
C06DBF has been prepared in the present form to complement a number of integral equation solving routines which use Chebyshev series methods, e.g., D05AAF and D05ABF.

9  Example

This example evaluates
0.5 + T1 x + 0.5 T2 x + 0.25 T3 x
at the point x=0.5 .

9.1  Program Text

Program Text (c06dbfe.f90)

9.2  Program Data


9.3  Program Results

Program Results (c06dbfe.r)

C06DBF (PDF version)
C06 Chapter Contents
C06 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012