% HERMITE INTERPOLATION ALGORITHM 3.3
%
% 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) )**2 * ... *
% ( X - X(N - 1) )**2 * (X - X(N) ).
syms('OK', 'FLAG', 'N', 'I', 'X', 'Q', 'A', 'NAME', 'INP');
syms('Z', 'K', 'J', 'OUP', 'XX', 'S','x','s');
TRUE = 1;
FALSE = 0;
fprintf(1,'This is Hermite interpolation.\n');
OK = FALSE;
while OK == FALSE
fprintf(1,'Choice of input method:\n');
fprintf(1,'1. Input entry by entry from keyboard\n');
fprintf(1,'2. Input data from a text file\n');
fprintf(1,'3. Generate data using a function F\n');
fprintf(1,'Choose 1, 2, or 3 please\n');
FLAG = input(' ');
if FLAG == 1 | FLAG == 2 | FLAG == 3
OK = TRUE;
end
end
if FLAG == 1
OK = FALSE;
while OK == FALSE
fprintf(1,'Input the number of data points minus 1\n');
N = input(' ');
if N > 0
OK = TRUE;
X = zeros(1,N+1);
Q = zeros(2*N+2,2*N+2);
for I = 0:N
fprintf(1,'Input X(%d), F(X(%d)), and ', I, I);
fprintf(1,'F''(X(%d)) on separate lines\n ', I);
X(I+1) = input(' ');
Q(2*I+1,1) = input(' ');
Q(2*I+2,2) = input(' ');
end
else
fprintf(1,'Number must be a positive integer\n');
end
end
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