E100 Polynomial Interpolation

Subroutine POLINT interpolates in a table of arguments $a$_j and function values $f$_j= f(a_j) , using an interpolating polynomial of specified degree K-1 which passes through K successive tabular points. The table arguments $a$_j 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 (N001), ABEND (Z035)

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, $(j=1,2,...,K)$ .

A

( REAL) One-dimensional array. A(j) must be equal to the table argument $a$_j,(j=1,2,...,K) .

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 $(a$_j,f_j),(j=1,2,...,K) .

Method:

Newton's divided difference formula is used.

Restrictions:

$2\; \le K\; \le 20$ . If $K>20$ , 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).
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E102