INTERPOLATION AND APPROXIMATIONT
Two Marks With Answers
1. Explain briefly Interpolation.
Ans: Interpolation is the process of computing the values of a function for any value of the independent variable within an interval for which some values are given.
2. Definition of Interpolation and extrapolation.
Ans: Interpolation: It is the process of finding the intermediate values of a function from a set of its values specific points given in a tabulated form. The process of computing y corresponding to x is interpolation.
3. State Newton’s Forward interpolation formula.
4. State Newton’s Backward interpolation formula.
5. Error in Newton’s forward:
6. Error in Newton’s Backward:
7. State Newton’s divided difference formula.
8. Show that the divided differences are symmetrical in their arguments.
10. Divided difference table:
11. Write Lagrangian’s polynomial formula.
12. What is the assumption we make when Lagrange’s formula is used?
Ans: It can be used whether the values of x, the independent variable are equally spaced or not whether the difference of y become smaller or not.
13. Write Lagrangian inverse interpolation formula.
14. Define Cubic Spline
Ans: Let , i = 0, 1, 2... n be the given (n +1) pairs of a data. The third order curves employed to connect each pair of data points are called cubic splines. (OR) A smooth polynomial curve is known as cubic spline.
15. Write down the formula of Cubic Spline.