E100: Polynomial Interpolation

Author(s): F. James	Library: KERNLIB
Submitter:	Submitted: 05.09.1966
Language: Fortran	Revised: 18.11.1985

Subroutine POLINT interpolates in a table of arguments and function values , using an interpolating polynomial of specified degree K-1 which passes through K successive tabular points. The table arguments need not be equidistant. Meaningful results can usually be obtained only for small values of K (typically less than 10).

Structure:

SUBROUTINE subprogram
User Entry Names: POLINT
Files Referenced: Printer
External References: KERMTR, ABEND

Usage:

    CALL POLINT(F,A,K,X,R)

F

(REAL) One-dimensional array. F(j) must be equal to the value at A(j) of the function to be interpolated, .

A

(REAL) One-dimensional array. A(j) must be equal to the table argument .

K

(INTEGER) K-1 is the degree of the interpolating polynomial.

X

(REAL) Argument at which the interpolating polynomial is to be evaluated.

R

(REAL) On exit, R is set equal to the value at X of the polynomial passing through the points .

If X lies outside the range of the points , the interpolation becomes an extrapolation, with consequent loss of accuracy.

Method:

Newton's divided difference formula is used.

Restrictions:

. If , the interpolation is performed as if K had the value 20. The original value of K is unchanged on exit.

Error handling:

Error E100.1: . A message is printed unless subroutine KERSET (N001) has been called.

Notes:

POLINT is intended for interpolation using all the tabulated points in the array A. To use only the tabulated points around the value of the argument X, use DIVDIF (E105).