Problems in Numerical Interpolation

For all problems, generate results based on linear and parabolic interpolations.

Estimate the error associated with linear interpolation.

1. Given that f(x) = 1/x, determine the Lagrange polynomial that will pass

through the points (2.0, 2.5, 3.5,4.0) and then determine the value of 1/3.

2. The following are certain values of the Bessel function of the first kind of

order zero:

x: 1.0 1.3 1.6 1.9

f(x): 0.7651977 0.6200860 0.4554022 0.2818186

Estimate f(1.5). Estimate also the true error if the true value is 0.5118277

3. Given that f(x) = 3x, determine the Lagrange polynomial that will pass

through the points (–2.0, –1.0, 0, 1.0) and then determine the value of square root of 3

4. In a radiation experiment, the dosage at various positions in the apparatus

are recorded as follows:

position (inch): 0 0.5 1.0 1.5 2.0 3.0 3.5 4.0

dosage (105 rads/hr): 1.90 2.39 2.71 2.98 3.20 3.20 2.98 2.74:

Estimate the missing value at position 2.5 inch.

5. Using the logarithm values of 654, 658, 659, and 661, determine the

logarithm value of 656. Calculate also the percent true error associated with the

answer.