Thapar University 2006 B.E Computer Science Numerical Analysis - Question Paper

Ka)

(b)

What is the loss of significant figures? How do you overcome with this difficulty whenever it occurred during computation? Elaborate with appropriate example.

_D r² h

If in the formula K = H, the percentage error in R is not to exceed 0.3%. Find the 2 h 2

allowable percentage error in r and h, when r = 48 mm and to = 56 mm.

5

(5)

2(a)

(b)

Prove that the order of convergence of Secant method is 1.618.

Show that x = 1 + tan¹ x has a zero in the interval 1, 1 + .Is this interval

L ²J

contains fixed - point such that for any x₀ the iteration function at_/|+1 = 1 + tan¹ x_n, n > 0 will converge to unique solution? If yes, find the solution correct to three decimal places.

(5)

(5)

3(a)

(b)

If /(x) be a function defined on [a,b] and set of nodes follow

a = x₀ < x, <  < x_n = b. Write all the six conditions so that g(x) becomes

the cubic spline interpolant for /(*).

Given that

x 1.0 1.5 2.0 log x: 0.0 0.17609 0.30103 Find log 1.8 using Newton divided interpolation formula

(4)

(6)

4(a)

(b)

Show that Gauss elimination method applied to a system of order n requires n{n l)/ 2

divisions, rt(²-l)/2 multiplications and n{n^Z -1)/2 additions operations in reducing the system into triangular form.

Solve the following system of equations using Crouts triangularization method

x, + x₂ + = 1 ; 2xj + 3x₂ - x₃ = 6; 3x, + 5x₂ + 3x₃ = 6

(4)

(6)