# interpolating polynomial in a sentence

### Examples

- For every absolutely continuous function on the sequence of
*interpolating polynomials*constructed on Chebyshev nodes converges to " f " ( " x " ) uniformly. - The disadvantage of Lagrange representation is that any additional point included will increase the order of the
*interpolating polynomial*, leading to the need of recomputing all the fundamental polynomials. - Does there exist a single table of nodes for which the sequence of
*interpolating polynomials*converge to any continuous function " f " ( " x " )? - Moreover, the
*interpolating polynomial*is unique if and only if the number of adjustable coefficients is equal to the number of data points, i . e ., " N " = 2 " K " + 1. - Lyness and Moler showed in 1966 that using undetermined coefficients for the polynomials in Neville's algorithm, one can compute the Maclaurin expansion of the final
*interpolating polynomial*, which yields numerical approximations for the derivatives of the function at the origin. - There is some subtlety in how one treats the a _ { N } coefficient in the integral, however to avoid double-counting with its alias it is included with weight 1 / 2 in the final approximate integral ( as can also be seen by examining the
*interpolating polynomial*):