In: Computer Science
Using the method of undetermined coefficients, derive an interpolation polynomial f(x) of the form "a +bx", for the following data. Determine the interpolation value of f(0.52).
x 0.45 0.55 0.65 0.75
y 0.075 0.136 0.227 0.372
We can make the coeffcient matrix A and vector B
such that AX=B will give solution to a and b
So,
A =
0.4500 1.0000
0.5500 1.0000
0.6500 1.0000
0.7500 1.0000
B =
0.0750
0.1360
0.2270
0.3720
So,
X=A\b
So,
X =
0.9820
-0.3867
Where b=0.9820 and a= -0.3867
So,
f(x)=a+b*x
So, f(0.52)=0.1239