University of Sargodha BS 6" Term Examination 2015 Subject: Computer Science Paper: Numerical Computing (MTH-310) Time Allowed: 2:30 Hours

University of Sargodha

BS 6" Term Examination 2015

Subject: Computer Science Paper: Numerical Computing (MTH-310)

Time Allowed: 2:30 Hours

Maximum Marks: 80

Objective part is compulsory. Attempt any four questions from subjective part.

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Objective Part

(Compulsory)

Q.1 White short anowers of the following questions

What is numerical method? -

11. A Define absolute error and relative error —

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iii. y What are significant digits? -

IV.

How the errors in initial numbers are propagated further through arithmetic operations?

v. With initial guess range [3, 5] for the root of X? - 1L find the next range as given by bisection

method.

vi. * Explain geometrically, how the choice of guess for new root is made in any iteration of

Newton-Raphson method.

vii. Explain the drawbacks of Gauss elimination method. -

vili. i

Explain the nature of Eigen-systemp

ix. • What is an interpolation?

• What is least square fit? —

Xia What is numerical differentiation?—

xii.

Give usefulness numerical integration.

xili. State Trapezoid rule of integration.-

xiv.

What is Monte Carlo numerical method?

explain polynomial interpolation with its general form.—

xVi.

Explain pivoting and its uses.

Q.2

Q. 3

Q.4

Q.5

Q. 6

Q.7

Subjective Part

(4*12)

Write a C++ program to input given 3x3 matrix A and 3xl column vector B elements to

compute unknown vector X elements. While solving a 3x3 system

simultaneous linear equations.

AX = B of

[Hints: write function to read matrix A and a function to

read vector B elements, then call these functions in main program]

(12]

Write an algorithm of Bisection method considering an interval, error limit as input. (12]

Give the basic idea in solving a set of lincar simultaneous equations using the Gauss

elimination method. Explain the steps of the method in details.

State trapezoidal rule of integration. Drive it and write C++ program. to compute integration of

given function data. Consider the function data as input.

What are forward differences and forward differences tables?

Give the outline of solving a matrix eigen-equation by polynomial method

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(12]

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