سوال ۲۴ کنکور ارشد علوم کامپیوتر ۱۴۰۰

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

As we have seen, every spline is underdetermined by the requirements of interpolation; extra information must be supplied. All too often programs for spline interpolation do not allow the user to supply this and one may be led to believe that it is not necessary. Rather, the code has built in specific assumptions: a natural spline is the easiest choice, but others are possible too. For example, a program may estimate first derivatives at the two ends from the data and use these for $d_1$ and $d_n$. When not required to give any extra conditions, the user should be alert to study the program documentation to discover which defaults are being used.

The extra information for construction of a spline ----------.

1. is the deciding choice for the type of the intended spline
2. is always decided by the construction program
3. is used as the first derivative estimates at the endpoints
4. is always set to yield a natural spline