NEWTON_ INTERPOLATORY
2016-08-23
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TO OBTAIN THE DIVIDED-DIFFERENCE COEFFICIENTS OF THE INTERPOLATORY
POLYNOMIAL P ON THE (N+1) DISTINCT NUMBERS X(0), X(1),..., X(N)
FOR THE FUNCTION F:
INPUT NUMBERS X(0),X(1),...,X(N); VALUES F(X(0)),F(X(1)),...,
F(X(N)) AS THE FIRST COLUMN Q(0,0),Q(1,0),...,Q(N,0) OF Q.
OUTPUT THE NUMBERS Q(0,0),Q(1,1),...,Q(N,N) WHERE
P(X) = Q(0,0)+Q(1,1)*(X-X(0))+Q(2,2)*(X-X(0))*(X-X(1))+
...+Q(N,N)*(X-X(0))*(X-X(1))*...*(X-X(N-1)).
POLYNOMIAL P ON THE (N+1) DISTINCT NUMBERS X(0), X(1),..., X(N)
FOR THE FUNCTION F:
INPUT NUMBERS X(0),X(1),...,X(N); VALUES F(X(0)),F(X(1)),...,
F(X(N)) AS THE FIRST COLUMN Q(0,0),Q(1,0),...,Q(N,0) OF Q.
OUTPUT THE NUMBERS Q(0,0),Q(1,1),...,Q(N,N) WHERE
P(X) = Q(0,0)+Q(1,1)*(X-X(0))+Q(2,2)*(X-X(0))*(X-X(1))+
...+Q(N,N)*(X-X(0))*(X-X(1))*...*(X-X(N-1)).
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newton
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