Tamil Nadu Open University (TNOU) 2006 B.C.A Computer Application Computer oriented numeric methods - Question Paper
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UG-725 BCA-12
B.C.A. DEGREE EXAMINATION - JUNE 2006.
Second Year
(For Candidates admitted in AY-200405 only)
COMPUTER ORIENTED NUMERICAL METHODS
Time : 3 hours Maximum marks : 60
PART A (4 x 5 = 20 marks)
Answer any FOUR questions.
1. Perform 3 iterations of fixed point iteration method to find the smallest positive root of the equation.
xz - 3x + 1 = 0 by starting at x0 = 0.5.
2. Explain Jacobis iterative method and sufficient condition for convergence of the Jacobi method.
3. What is Inverse Interpolation? Find the value of x when y = 3.
x 4 7 10 12
Y -\ 1 2 4
4. Prove the uniqueness of the interpolating polynomial by applying suitable results.
5. Find Newtons backward difference form of interpolating polynomial for the data given below :
x 4 6 8 10
f(x) 19 40 79 142
Hence interpolate f (9).
6. Discuss briefly the various types of errors that will arise in numerical calculation.
PART B (4 x 10 = 40 marks)
Answer any FOUR questions.
7. Perform three iterations of second method to solve x3 + x - 6 = 0. Starting with x0 = 1 and xx 2.
8. Find the iteration function g (x) and corresponding interval to get the two roots 1 and 2 by fixed point iteration method for the equation x2 -3x + 2 = 0.
9. Solve the system of equations by Gauss elimination.
xl - x2 + 2x3 - x4 = - 8 2xt - 2x2 + 3xa - 3x4 = - 20 x + x2 + x3 + 0x4 = - 2 xl-x2 + 4x3 + 3x4 = 4
10. Using forward differences show that the following data represents a third degree polynomial.
-3-2-1012 3
fix) -29 -9-113 11 31
Find the polynomial and obtain the value of
11. (a) Explain interpolation and extrapolation.
(b) Discuss briefly Lagranges form of interpolating polynomial.
12. (a) State intermediate value theorem.
(b) Find a root by Bisection method which lies between 0 and 1.
at3 -5*+ 1 = 0.
3 UG-725
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Earning: Approval pending. |