سوال ۲۲ کنکور ارشد علوم کامپیوتر ۱۴۰۰

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

Given a specific data set to interpolate, a few general guidelines can be suggested for deciding between these two similar piecewise polynomial interpolations. Of course, 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 involves the whole lime and effort required should be considered. An Hermite cubic interpolant is also defined by coefficients, but these are obtained without solving a linear system.

In general, it is expected ----------.

1. an Hermite cubic interpolant to be discontinuous
2. an Hermite cubic interpolant to be smoother than a spline
3. a spline to be smoother than an Hermite cubic interpolant
4. to have more computing effort for construction of an Hermite cubic interpolant than a spline