سوال ۲۱ کنکور ارشد علوم کامپیوتر ۱۴۰۰

PASSAGE 2: PRACTICAL DIFFERENCES BETWEEN SPLINES AND CUBIC HERMITES (excerpt)

... If smoothness of the second derivative is required then splines are selected, but usually this is not demanded explicitly. For "nice" data sets there is little qualitative difference between the two interpolants. But it is sometimes possible to notice that the cubic Hermite is less smooth. To obtain a spline we must solve a system of equations for the coefficients. This is fast as mentioned above, but the system must be set up and the time and effort required should be considered. An Hermite cubic interpolant is also defined by coefficients, but these are obtained without solving a linear system. ... If the derivatives of the interpolant or model are known then these may be easily incorporated into the Hermite cubic but not easily into the spline, unless the derivatives occur at the endpoints. If the derivatives are not known then various estimates of them can be computed and used; effort is required here too.

According to the passage, a Hermite cubic interpolant ----------.

1. is often smoother than a spline
2. cannot incorporate second derivative information
3. can easily accommodate a model with known derivatives
4. requires excessive computing effort to be constructed