PCOEF()
by Carlie J. Coats, Jr., Ph.D.
Fortran version:
SUBROUTINE PCOEF( N, XN, YN, CN )
INTEGER N ! length of input vector
REAL XN( N ) ! input vector of X-values
REAL YN( N ) ! input vector of Y-values
REAL CN( N ) ! output vector of polynomial coefficients
C version: none
Summary:
PCOEF() finds the array CN of coefficients for the polynomial P going
through the sets of points <XN( k ), YN( k )>, k = 1,...,N.
Must have N < 16; in practice, N should not exceed
8, and the points XN( k ) should be well-spaced-out, or numerical
instabilities may arise. To evaluate P at X, evaluate the sum
SUM( CN( K ) * X**(K-1) ; K = 1,...,N )
Note that the following code ( the "Horner trick") is an
efficient way to evaluate this in Fortran:
...
Y = CN( N )
DO 11 K = N-1, 1, -1
Y = X * Y + CN( K )
11 CONTINUE
...
See also POLY.
Fortran Usage:
!! under construction !!
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