University of Sargodha BS 5* Term Examination 2012 Subject: Computer Science Paper: Numerical Computing (CS-3941)

University of Sargodha

BS 5* Term Examination 2012

Subject: Computer Science

Paper: Numerical Computing (CS-3941)

Time Allowed: 2:30 Hours

Maximum Marks: 80

Note: Objective part is compulsory. Attempt any three questions from subjective part.

Objective Part

(Compulsory)

(st Write short answers of the following in 2-3 lines each on your answer sheet.

(16*2)

Explain exponential curve.

il:

iii.-

What is Lagrange polynomial?

iv.*

Write steps of power method for Eigen values.

Define interpolation.

V=

Write any formula of numerical differentiation.

vir

Define numerical integration.

ustadni.com

vii.- Define backward difference in interpolation.

viii.- Explain the Gaussian elimination method.

ix:

What are zeros of polynomial?

xi.

Explain the least square method.

What are the normal equations of straight line?

xii: Explain error analysis for iterative method.

xili: Define algorithms and convergence.

xiv. Explain techniques for solving linear system of equations.

xv. Define orthogonal polynomials with example.

xvi. Provide an example of improper integrals.

Subjective Part

(3*16)

Q.2. Compute the Eigen values and associated Eigen vectors of the following matrix

1

A=

2

0

0

Q.3. By using the method of least squares, find a relation of the form y = ax" that fits the data

2

3

4

5

Q.4.

27.8

62.1

110

Show that the polynomial interpolating the following data has degree 3

S'X

-2

-1

1

161

3

f(x)

1

4.

11

16

13

400

Q.5.

Q.6.

Compute f"(O) and f'(2) from the following tabular data

0.00

0.2

0.4

0.8

1.0

f(x)

1.00

1.16

3.56

13.96

41.96

101.00

Prove the following statements or provide counterexample to show they are not true

a) The product of two symmetric matrices is symmetric

b) The inverse of a nonsingular symmetric matrix is a nonsingular symmetric matrix

c) If A and B are nxn matrices. Then (AB)' = A'B'

visit website: ustadni.com