"CODE"36010;
"PROCEDURE" NEWTON(N,X,F);
"VALUE" N; "INTEGER" N; "ARRAY" X,F;
"COMMENT" NEWTON DETERMINES THE COEFFICIENTS C[J],J=0,...N,
OF THE INTERPOLATION POLYNOMIAL C[0] + C[1] *(X-X[0])+...+
C[N] * (X-X[0])*...*(X-X[N-1]) OUT OF N+1 LIN. EQUAT.
THE ARGUMENTS AND FUNCTION VALUES MUST BE GIVEN IN
ARRAY X, F[0:N]. THE ARRAY F IS OVERWRITTEN BY
THE COEFFICIENTS C[J],J=0,...N;
"BEGIN" "INTEGER" K,I,IM1;
"REAL" XIM1,FIM1;
IM1:=0;
"FOR" I:= 1 "STEP" 1 "UNTIL" N "DO"
"BEGIN" FIM1:=F[IM1];XIM1:=X[IM1];
    "FOR" K:= I "STEP" 1 "UNTIL" N "DO" F[K]:= (F[K]-FIM1)/(X[K]-XIM1);
    IM1:= I
"END"
"END" NEWTON;
        "EOP"