سوال ۲۲ کنکور ارشد علوم کامپیوتر ۱۳۹۹

Read the following passage and answer the question.

PASSAGE 2:

To put the problem of polynomial interpolation into a familiar framework, it is well-known, and perhaps obvious, that there is a unique straight line passing through any two points in the plane. This straight line is (the graph of) the linear, or first-degree, interpolating polynomial for this data, the coordinates of the two points. In precisely the same way it is easy to show that there is a unique parabola which passes through any three points: this is the graph of the quadratic, or second-degree, interpolating polynomial which agrees with the given data. In general, we will find that there is a unique polynomial of the minimum possible degree n which agrees with a given function at n − 1 data points, or nodes.

The drawbacks of this polynomial interpolation approach include the following. If the number of data points is large, then the degree of the interpolating polynomial will be high and therefore its evaluation will itself be computationally expensive. Second, few physical laws are of high-degree polynomial nature, and so the approximating function is likely to exhibit less subtle behavior than the function or phenomenon being approximated. (Note that high-degree polynomials will often have many turning points, which is again untypical of physical phenomena.) The use of a single interpolation polynomial over a wide range gives equal weight to function values distant from the point of interest as it does to those at nearby points.

Question: Polynomial interpolation of large number of data points is ----------- of the interpolating polynomial.