HERMITE ALGORITHM
2016-08-23
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TO OBTAIN THE COEFFICIENTS OF THE HERMITE INTERPOLATING
POLYNOMIAL H ON THE (N+1) DISTINCT NUMBERS X(0),...,X(N)
FOR THE FUNCTION F:
INPUT NUMBERS X(0), X(1),..., X(N); VALUES F(X(0)), F(X(1)),...,
F(X(N)) AND F'(X(0)), F'(X(1)),..., F'(X(N)).
OUTPUT NUMBERS Q(0,0), Q(1,1),..., Q(2N+1,2N+1) WHERE
H(X) = Q(0,0)+Q(1,1)*(X-X(0))+Q(2,2)*(X-X(0))**2+
Q(3,3)*(X-X(0))**2*(X-X(1))+Q(4,4)*(X-X(0))**2*
(X-X(1))**2+...+Q(2N+1,2N+1)*(X-X(0))**2*
(X-X(1))
POLYNOMIAL H ON THE (N+1) DISTINCT NUMBERS X(0),...,X(N)
FOR THE FUNCTION F:
INPUT NUMBERS X(0), X(1),..., X(N); VALUES F(X(0)), F(X(1)),...,
F(X(N)) AND F'(X(0)), F'(X(1)),..., F'(X(N)).
OUTPUT NUMBERS Q(0,0), Q(1,1),..., Q(2N+1,2N+1) WHERE
H(X) = Q(0,0)+Q(1,1)*(X-X(0))+Q(2,2)*(X-X(0))**2+
Q(3,3)*(X-X(0))**2*(X-X(1))+Q(4,4)*(X-X(0))**2*
(X-X(1))**2+...+Q(2N+1,2N+1)*(X-X(0))**2*
(X-X(1))
fortran
算法
埃尔米特
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