The higher the degree of the interpolating polynomial, the faster the convergence.

2.

The interpolating polynomial should approximate the given function.

3.

Calculating the interpolating polynomial is computationally expensive ( see computational complexity ) compared to linear interpolation.

4.

Choosing the points of intersection as interpolation nodes we obtain the interpolating polynomial coinciding with the best approximation polynomial.

5.

Additionally, the interpolating polynomial is unique, as shown by the unisolvence theorem at the polynomial interpolation article.

6.

For more information on formulation of trigonometric interpolating polynomials in the complex plane see, p135 Interpolation using Fourier Polynomials.

7.

It does not require an interpolating polynomial but instead one has to evaluate the derivative f'in each iteration.

8.

Neville's algorithm is based on the Newton form of the interpolating polynomial and the recursion relation for the divided differences.

9.

With the Newton form of the interpolating polynomial a compact and effective algorithm exists for combining the terms to find the coefficients of the polynomial.

10.

This is indicative of how large degree interpolating polynomial Newton Cotes methods fail to converge for many integrals, while Romberg integration is more stable.

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