F G192147 Pages:3
Reg No.: Name:
APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
SEVENTH SEMESTER B.TECH DEGREE EXAMINATION(R&S), DECEMBER 2019
Course Code: CE473
Course Name: Advanced Computational Techniques and Optimization
Max. Marks: 100 Duration: 3 Hours
PART A
Answer any two full questions, each carries 15 marks. Marks
1 a) Briefly explain different numerical methods to solve the system of linear (5)
algebraic equations.
b) Obtain by Power method the numerically dominant eigen value and eigen vector (10)
15 -4 2
of the matrix [A] = ۶ 12 -6 |. Take the initial approximation as [1 1 11.
-20 4 -2
2 a) Explain general procedure in optimization techniques (5)
b) Find the minimum point of the function using multi-variable unconstrained (10)
optimization technique, / = 2:2 + xy + 12 +)2+ 22 - 6 - 7), -82 +9
3 9) Apply Gauss Seidel iteration method to solve the equations : (8)
10x + ‏بر‎ + 22 = 44; 2x + ‏+مر2 + : [ذ- 2 + م0[‎ 102 = 61
b) Determine the maximum and minimum value of the single variable function (7)
f(x) =12x° —45x* +40x° +5
PART ‏تا‎
‎Answer any two full questions, each carries 15 marks.
4 a) Acurve passes through the points (0,18), (1,10), (3,-18) and (6,90). Find the slope (7)
of the curve at x = 2 using Lagrangian interpolation.
1: 1 1 ⋅
b) Evaluate So Tay ‏حل‎ using (8)
a) Trapezoidal rule , take h= 1/4
b) Weddle’s rule , take h=1/6
5 a) Using Simplex method, maximize £ = 8000 x + 12000 (7)

subject to the constraints:
3x + 47 < 60
x + 3y < 30

x20, } <0

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