Short Questions and Answers

SHORT QUESTIONS AND ANSWERS

1. Derive Newton's backward difference formula by using operator method. [A.U, May, 1999, CBT N/D 2010]

Solution :

2. Derive Newton's forward difference formula by using operator method. [A.U N/D 2010]

Solution:

3. State Gregory-Newton forward difference interpolation formula.

 [A.U Tvli M/J 2011] [A.U M/J 20131 [A.U. M/J 2006, N/D 2011, N/D 2012] [A.U N/D 2013]

Solution:  

See Q.No. 2.

4. State Newton's backward difference interpolation formula.logsotni [A.U N/D 2009, CBT M/J 2010] [A.U N/D 2014 NM]

Solution:

See  Q.No. 1.

5. Using Newton's backward difference formula, write the formulae for the first and second order derivatives at the end value x = Xn upto the fourth order difference term.

Solution :

6. When Newton's backward interpolation formula is used? 12 [M.U. Oct. 1997, A.U N/D 2010] [A.U A/M 2019 R-17]

Solution:

The formula is used mainly to interpolate the values of y near the end of a set of tabular values and also for extrapolating the values of y a short distance ahead (to the right) of y_n.

7. Newton's forward interpolation formula used only for ................... intervals. [M.U. Oct., 1999]

Solution :

Equidistant intervals (or) equal intervals

8. Say True or False.

Newton's interpolation formulae are not suited to estimate the value of a function near the middle of a table.

Solution: True

9. Say True or False.

Newton's forward and Newton's backward interpolation formulae are applicable for interpolation near the beginning and end respectively of tabulated values.

Solution:  The statement is true.

10. Given f(0) = -2, f(1) = 2 and f(2) = 8. Find the root of the Newton's interpolating polynomial equation. f(x) = 0

Solution :

11. When will we use Newton's forward interpolation formula ?OREX [A.U N/D 2010] [A.U A/M 2019 R-17]

The formula is used to interpolate the values of y near the beginning of the table value and also for extrapolating the values of y short distance ahead (to the left) of y₀

12. What is the error in Newton's forward interpolation formula? [A.U. Tvli. M/J 2010]

Solution :

13. What is the error in Newton's backward interpolation formula?

Solution :

14. Give the relation between the divided differences and forward or backward differences.

Solution :

15. Find the polynomial which takes the following values given f (0) = −1, f(1) = 1 and ƒ (2) = 4 using the Newton's interpolating formula.

Solution :