سوال ۱۷ کنکور ارشد ریاضی ۱۴۰۱

PASSAGE 1 (excerpt):

"Another problem closely related to interpolation arises when the function values of $\phi$ at the net points $x_k$ are known only up to a certain error, the maximum magnitude of which is a priori known at each of the points. In this case, we want to construct a curve which would be in some sense the best approximation of the function, the latter being specified at the net points up to random errors. Problems of this kind are usually solved by the least-squares method."

(Earlier the passage notes that interpolation algorithms for the exact data are based on Lagrange interpolation polynomials, and that if the difference solution is obtained with a certain accuracy, the accuracy of the interpolation must be at least as high.)

17- When the function values at the data points are known to have errors, ---------- may appropriately be employed.