La grange interpolation polynomial
Programming

Tutor: None Selected  Time limit: 4 Hours 
DESCRIPTION
Application to chemical engineering
The density of the potassium carbonate aqueous solution varies with temperature and concentration. In an experiment to determine the density of carbonate was considered constant temperature and concentration was varied , giving the table:
x y
4 1.0276
12 1.1013
20 1.1801
28 1.2652
38 1.3480
45 1.4120
Write Scilab function is to use the Lagrange interpolation polynomial of the first degree to interpolate the value given by the user using the values of the vectors " x " and "y" passed as parameter.
To improve the approximation , the function must find the two values of X closest and use them in the polynomial . For example , if the user indicates that he wants to interpolate the value 25 , the program must use X0 = X1 = 20 and 28.
Example of program execution :
à x = [4 , 12, 20 , 28, 38 , 45] à y = [1.0276, 1.1013 , 1.1801 , 1.2652 , 1.3480 , 1.4120 ] à lagrange (25, x , y)
X values that were used to interpolate are 20 and 28 The estimate of 25 is 1.2332875
à lagrange (15, x , y) X values that were used to interpolate are: 12 and 20
The estimate of 15 is 1.13085
à lagrange (50, x , y) can not get an estimated 50 .
à lagrange (2, x , y) can not get an estimated 2
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