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Question: algorithm hermite interpolation 33 to obtain the coefficients of the...

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ALGORITHM Hermite Interpolation 3.3 To obtain the coefficients of the Hermite interpolating polynomial H(x) on the (n 1) distinct numbers xo, . xn for the function f: INPUT numbers xo, xi. . . .n; values f(xo OUTPUT the numbers Q0.0. Qi.1 , f() and f(xo), . .. , f(n) where + Q44(x - xo)-(r -xi2... Step 1 For i = 0, 1, … , n do Steps 2 and 3 Step 2 Set z2i = Xi; Q21.0 = f(xi); Q2i +1.0 = f(x); Q2i+1,1 = f,(xi) 0 then set Step 3 If i 2i.1 32i 22i- Step 4 Fori 2, 3, ,2n 1 Qij-1--1.j-I for j = 2.3. . . . ,i set Qi.j Step 5 OUTPUT (Qo,o. Q1,1.. . Q2n+1.2+ STOP

Write a MATLAB function to implement the Hermite interpolation in Algorithm 3.3. Note that the index should run from 1 instead of 0 that is used in the textbook. This is because MATLAB does not allow index 0 Your function should use the same order of input below. Note that we do not return Q as in the algorithm. Instead, we calculate the interpolated function value at x. function y hermite (X,Y,YF,x) = X=number3 x 1 x 2 x n %-= value3 f(x 1) f(x 2) f(x n) x-interpolation, (x2) f(x y ïnterpolated function value at x, i.e. H(x) x 2) .. x n) x = interpolation point X your implementation below end Save your function in hermite.n, and interpolate the tabular function given below at the point x 1.25. f(r) 110517 f (x) 0.22103 0.59673 147576 1.0 2.0 2.45960 Your function should return 1.1690.

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