سوال ۲۳ 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 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. Usually though, the choice between spline or Hermite cubic interpolation does not depend upon the amount of work to compute the d_i. ... 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 spline ----------.

1. is always preferred to an Hermite cubic interpolant
2. is not chosen when derivatives at the endpoints are to be set
3. is not preferred because its construction requires a system of equations to be solved
4. is the choice as an interpolant when second derivatives are to be smooth