Maximum Marks: 80 University of Sargodha BS s" Term Examination 2020 Subject: Computer Science

Maximum Marks: 80

University of Sargodha

BS s" Term Examination 2020

Subject: Computer Science

Paper: Numerical Computing (CS-3941)

Time Allowed: 2:30 Hour

ustadni.CObective part is compulsory. Attempt any three questions from subjective part.

Objective Part

Of (Compulsory)

Write short answers of the following in 2-3 lines each.

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i. com

ii. What is a fixed point for a function f(x)?

ili. What is the minimum number of data points required to pass through, to interpolate with a

polynomial of degree n?

iv. Let A be a symmetric matrix. Give an example when A - AT.

v. Why trapezoidal method is better that rectangular method?

vi. What is a convex function?

vii. In which method, we approximate the curve of solution by the tangent in cach interval?

Vili. What is the source of quantization errors in numerical computations?

ix. What is a cubic spline?

x. What do we mean by conditional convergence?

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xi. Consider a vector v - [10-30 20]. Give its [vili and liv ll..

Xii. What is the difference between a boundary value problem and initial value problem?

xili. What is the order of approximation using central difference formula for differentiation?

xiv. When Newton's method does not work well, while solving nonlinear equation with single

variable?

xv. Which method is used for interpolation when number of data points is greater than the order of

the polynomial?

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xvi. What is the bencfit of using secant method over Newton's method while finding roots of

nonlinear equation in one variable?

Subjective Part

(3*16)

Q.2. Evaluate S, cosh(x) dx by trapezoidal rule. Show 3 iterations.

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0.3. Numerically compute the second derivative of f(x)-cosh(x) and estimate error.

Q.4. Consider f(x) = e, and interpolate it by a parabola (N=2) from three samples at xo- -1; x; =0;

x2=1. Use Lagrange method.

Q.5. Consider equations x,?+ x3'=1, x2 = sin(x). Compute the solution using Newton's method.

Give two iterations only.

Q.6. Write algorithm to find eigenvalues using power method.

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