M.Sc. (Semester (CBCS) Examination Nov/Dec-2018
Computer Science
NUMERICAL ANALYSIS
iI
Time 2½ Hours Max. Marks: 70
Instructions: All questions are compulsory.
Figures to the right indicate full marks.
Q.1 Multiple choice questions. 14
Which of following symbol is called forward difference operator?
Δ ∇
δ E
What type of eigen value can be obtain using power method?
Largest eigen value Smallest eigen value
Eigen vector Characteristic equation
Lagrange's polynomial for interpolation can be used even if
Given argument are not equally spaced
Extrapolation to be done
Inverse interpolation is to be done
All of above
In application of Simpsons 1/3rd rule, interval h for closer approximation
should be
Odd Small
Even None of these
While evaluating definite integral by trapezoidal rule, accuracy can be
increased by taking
h 4 large number of subinterval
even number of subinterval has multiple of 3
A square matrix A is upper triangular if
aij 0 j i aij 0 i
aij 0 j aij 0 i
Relation between ∇ and E is given
E 1 − Δ 1 − E−1
E)−1 E − 1
Convergence in modified Eule+ method is than that of Euler's
method.
slower compatible
faster one time more
A differential equation together with initial conditions is called
Initial value problem Initial value
Conditional problem Problem
10) Backward difference operator is
− − − 8
− − −
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11) Method of false position is called
Regula falsi Runge kutta method
Euler's method Picard's method
12) Householder's method is used to obtain eigen values of matrices.
symmetric skew symmetric
diagonal triangular
13) The order of errors of Simpson's 1/3rd Rule for numerical integration with step
size h is
h2 h
h3 h4
14) The number of significant digits in number 24.0201 is
6 4
2 3
Q.2 Answer the following. (Any four) 08
Define R round off error.
Find divided difference of 2
1 3
4 32
Define initial value problem.
State Newton's Backward difference formula.
Write formula for Trapezoidal rule.
White notes on. (Any two) 06
Errors
Finite differences
Rate of convergence
Q.3 Answer the following. (Any two) 08
Explain Euler's method.
Prove that −

2
− − −
Find root of equation − − 5 0 using Newton Rapson method.
Answer the following. (Any one) 06
9
8
Solve following system using LV decomposition method.
6
1
− 5
− − 10
Solve following equation by Guass-Elimination method.
Q.4 Answer the following. (Any two) 10
Show that
Factorize the matrix

2 3 1
1 2 3
3 1 2
into LU form
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Answer the following. (Any one) 04
1 24 3 120 5 336 7 720
Find cubic polynomial for
Evaluate sume S 3 5 7 to 4 significant digits find its
absolute relative errors.

Q.5 Answer any two. 14
Derive Lagrange's interpolation formula.
I correct upto three decimal places. 0.1.25
Explain Newton Raphson method.