Question

Please help with this question. (Civil Engineering: Numerical Methods)

Suppose additional data points are expected, choose an appropriate method from Lagrange and Newton's divided differences methods for interpolation, and explain why.

Answer 1

If we see the formula of Lagrange interpolation, it is quite complex and lengthy. If the values given for data is more, generally more than four, it is become so much difficul for calculating. There is a chance of errror during calculaion if there is additional data points are expected. There is no chance to predetermine the polynomial degree untill the the calculation is over. So due to these problems, when there is additional datas's are expected genrally more than four values, langrange interpolation formula always avoid and Newton's divided difference is used.

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As in Newton's divided difference, we have to prepare the difference table by rearranging the values in ascending or descending order, and once the table is prepared , we can easily determine the function by the formula.If in any difference have come zero, then we can say that the degree of the polynomial without any calculation.

So that's why Newton's divided difference is always preferable when there is additional data points are expected to overcome the error and complex calculation.