Hermite Interpolation by polynomials

Please choose:

My own (x,y,y(1)) -data n= Important: 1 <= n <= 50 ! Degree is 2n+1 .

Please write your n+1 (x,y,y(1)) data here, values separated by blank or comma, no parentheses, each triple on a new line

Synthetic data

Choose a function:
f(x) = x2/3
f(x) = 1/(1+25x2)
f(x) = sin(2*pi*x)
f(x) = tanh(x)
f(x) = exp(x)
Input of a self defined function:
Please type the evaluation program of your function here using FORTRAN rules. Your final statement must be
      fu= some expression you computed before or just here depending on x
You may use the constants pi, e(=exp(1)), sqrt2(=1.414...), the integer variables i,j,k, the logicals bool1,bool2,bool3 and the double precision variables sum,h1,h2,h3,h4,y(100),z(100),a(100,100) which are all intialized with zero resp. .false. . The routine has the parameters x (double, input) and fu (double out). never change x!. first is a local integer and set 0 before calling the function the first time. You may use this in order to initialize some local data and set it 1 afterwards to avoid multiple such initialization. Your settings of the local variables are preserved during program execution.


Since the derivative values are computed automatically using JAKEF, your code must obey its restrictions!

Please specify the degree here:
n = Important: 1 <= n <= 50 !

Please specify the interval for the x-data [a,b]
a = b =

How should the x-data be distributed ?
equidistant (hence x(i)=a+(b-a)*i/n )
transformed Chebyshev abscissae
(hence (a+b)/2+(b-a)/2*cos((2i+1)pi/(2n+2)) )

use the derivative values of f
set derivative values to zero (Fejer interpolation)
automatically sets the Chebyshev nodes

Do not print divided differences
Print divided differences

Do not print the polynomial formula
Print polynomial formula

Click on "evaluate", in order to submit your input.

Back to the theory page

 Back to the top!

18.02.2015