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Interpolation is a method to estimate intermediate values between given precise data points

The figure above shows  both Interpolation and extrapolation. We are going to learn about Interpolation, the blue part of the region.  Extrapolation will not be covered.

The most common method used is known as polynomial interpolation.

For this chapter, you will be exposed to these two methods:

a. Newton’s Interpolating Polynomials

b. Lagrange Interpolating Polynomials

Kindlyy watch the interpolation videos is sequence, starting from First video, second video etc etc

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Curve Fitting - Second order Interpolation  - Part 1

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Curve Fitting - Second order Interpolation  - Part 2

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Curve Fitting - Higher order interpolation part 1

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Curve Fitting -  Higher order Interpolation - Part 2

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Before answering this question, be reminded to order your points  to attain optimal accuracy.  How to do that?? order the points so that they are as close to and as centered and balanced about the unknown (4)  as possible.

a) Calculate f(4) using Newton’s interpolating polynomials of order 1 through 4.

Answer: 59, 50, 48,48

b) Calculate f(4) using Lagrange polynomials of order
1 through 2.

Answer : 59, 50

The answers for 3rd and 4th order Newton's polynomial are the same. what conclusion can be drawn here?

Please drop your answer in the comments section

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The answer to the above question is:

a) 6.4527
b) 6.4534

Can somebody tell me which method gives less error, and why? You may drop yur answer in the comment section

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This is one of the final exam questions on Interpolation
Please spare some time to try this, your final answer should be

Concentration at 10 hr = 1.000045 kg/m3

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Determine v at T = 750 degrees F

Answer: 0.14831