Question

In: Computer Science

5.1 Using the method of undetermined coefficients, derive aninterpolation polynomial f(x) of the form "a...

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

Solutions

Expert Solution

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


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