Computer Oriented Numerical Analysis Assignment

8/10/2019 Computer Oriented Numerical Analysis Assignment

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Computer Oriented Numerical Analysis

Amity CampusUttar Pradesh

India 201303

ASSIGNMENTSPROGRAM: BSc IT

SEMESTER-II

Subject Name :

Study COUNTRY :

Roll Number (Reg.No.) :

Student Name :

INSTRUCTIONS

a) Students are required to submit all three assignment sets.

ASSIGNMENT DETAILS MARKS

Assignment A Five Subjective Questions 10

Assignment B Three Subjective Questions + Case Study 10

Assignment C Objective or one line Questions 10

b)

Total weightage given to these assignments is 30%. OR 30 Marks

c)

All assignments are to be completed as typed in word/pdf.

d)All questions are required to be attempted.

e)

All the three assignments are to be completed by due dates and need to

be submitted for evaluation by Amity University.

f)

The students have to attached a scan signature in the form.

Signature : _________________________________

Date : _________________________________

( ) Tick mark in front of the assignments submitted

Assignment

A

Assignment B Assignment C


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Assignment


Assignment A1. Define error, relative error and absolute error. Give example of each.

2. Find the rate of convergence of Newton Raphson Method.

3. By using Regula Falsi method find the root of 15 correct up to 2 decimal places.4. Solve the following set of equations by using Gauss Elimination Method.

2x+3y+4z = 12

3x+y+z = 4

x+4y+z = 55. Solve the following set of equations by Gauss Seidal Method.

-8x1+ x2+ x3= 4

x1+ -5x2x3= 1x1+ x24x3= 3

Assignment B

1. (a) Round off and truncate the following numbers to four decimal places.

(a)132.59839(b)0.073729

(c)9528.26058

(b)Find the root of the equation 2x3-5x-1=0 by using Bisection method. Perform

5 steps.

2.

Solve the following problem by Jacobi Method. Perform three steps.x1 - 2x2 - x3 - x4= 3

-2x1+x2- x3- x4= 15x1 - x2 +x3-2x4= 27

-x1-x2-2x3+x4= -9

3. (a) For the given data

x f(x)

1 33

2 50

3 69

4 905 129

Find the value of f(x) at 1.4

(b) Choose 4 cards at-random from a standard 52 card deck. What is theprobability that two kings and two ace will be chosen.


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Assignment C1. Round off the number 0.859378 to four significant digits.

(a) 0.8594 (b) 0.8593 (c) 8593 (d) 8.593

2. Truncate the number 0.859378 to four significant digits.

(a) 0.8594 (b) 0.8593 (c) 8593 (d) 8.593 (e) None

3. The formula for Regula Falsi method is

(a)x2=x1-(f(x0)(x1-x0)/(f(x1)-f(x0)) (b)x2=x1-(f(x0) (f(x1)-f(x0))/(x1-x0)(c)x2=x0-(f(x0)(x1-x0)/(f(x1)-f(x0)) (d)x2=x0-(f(x0) (f(x1)-f(x0))/(x1-x0)

4. Solve the following equation by Regula Falsi Method upto 2 steps by taking the initialvalue x0=1 and x1=2

X3-X-4=0

(a) 1.234 (b) 1.666 (c) 1.9823 (d) None of the above

5. Choose the initial values of the Bisection Method to solve the following equationx

5+5x+1=0

(a) x0=1, x1=2(b) x0=0, x1=1 (c) x0=0, x1=-1 (d) x0=-1, x1=-2

6. Solve x3-2x-5=0

by Newton Raphson Method upto 2 decimal places of accuracy by

taking x0=2(a) 2.3568 (b) 2.995 (c) 2.09 (d) 2.135

7. Solve x=1/(x+1)2by iteration method. Take x0=0.5. Perform two steps only.

(a) .479 (b) .3854 (c) .4053 (d) .793

8. Which method has the fastest convergence?(a) Bisection method (b) Newton Raphson Method (c) Regula Falsi Method

(d) Iterative Method

9. In Bisection method the initial approximation x0 and x1 are chosen such that

(a) f(x0).f(x1)0 (c) f(x0).f(x1)=0(d) f(x0)-f(x1) is negative.

10. The basic iteration formula to solve 12 is(a)1/2(xn-12/xn) (b) 1/2(xn+12/xn) (c) 1/2(1/xn-12/xn) (d) None

11. The equation 3-x=e(x-1)

is an example of(a) Transcendental equation (b) Algebraic Equation (c) Polynomial Equation


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(d) None of the above

12.4y0=

(a)y4-4y3+6y2-4y1+y0 (b) = y4-4y3+6y2-4y1+y0

(c) y4+4y3-6y2+4y1-y0 (d) None of these

13. Which one is true?

(a) E+ =1 (b) E- =1 (c) E* =1 (d) E/ =1

14. If ei+1/eip

= 1 then rate of convergence is said to be

(a) Linear (b) Quadratic (c) p (d) None

15. Rate of convergence of Newton Raphson method is

(a) 1 (b) 2 (c) 3 (d) Cant be determined

16. Inverse of inverse of a matrix A is

(a) A-1

(b) 1/A (c) A (d) None of these

17. For Matrix A and B of same order, AB=BA(a) True (b) False (c) Cant be determined (d) None of these

18. Which one is true?(a) y1=y0-h (b) y1=y0/h (c) y1=y0+h (d) None

19. Which one is an integration method?(a) Trapezoidal Method (b) Newton Raphson Method (c) Jacobi Method (d) None

20. Which one is not an interpolation method?

(a) Lagranges Method (b) Newton Forward Method(c) Newton Divided Difference Formula (d) Bisection Method

21. Round off the number 0.259378 to four significant digits.(a) 0.2594 (b) 0.2593 (c) 2593 (d) 2.593 (e) None

22.Truncate the number 0.159378 to four significant digits.(a) 0.1594 (b) 0.1593 (c) 1593 (d) 1.593 (e) None

23. The formula for Bisection method is(a)x2=(x0+x1)/2 (b) x2=(x0-x1)/2(c)x2= x2=(x0*x1)/2 (d)None

23.Cramers rule fails for

(a) = 2 (b) = 1 (c) =0 (d) None

24.To solve a set of linear algebraic equations, the method is:


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(a) Gauss Jordan (b) Jacobi (c) Gauss Elimination (d) All

(e) None

25. Eigen values for 1 4 will be3 2

(a) (1,6) (b) (2,3) (c) (2,2) (d) None

26.Equation of line is:

(a) y=c (b) y=ax2+c (c) y=ax+c (d) None

27.2y0is

(a) y2-2y1+y0 (b) y2+2y1+y0 (c) y2+y1+y0 (d) None

28.Runga Kutta method is used for(a) Differentiation (b) Integration (c) Differential Equation

(d) None of these

29.Trapezoida formula is(a) h/2[y0+yn+2(y1+y2+.+yn)] (b) [y0+yn+2(y1+y2+.+yn)]

(c) 3h/8[y0+yn+2(y1+y2+.+yn)] (d) None of these

30.For Simpsons 3/8 rule, the value of n is

(a) 1 (b) 2 (c) 3 (d) 4

31.Accuracy of Simpsons method is better than Trapezoidal method.

(a) True (b) False (c) Cant say

32.

Divided Difference formula can also be used for equi-distant points:(a) True (b) False (c) Cant say

33. (1+)(1+)=

(a) 0 (b) 1 (c) (d) None

34. Given the data

x 1 2 3

F(x) 2 5 8

What is the value of F(x) at x=1.5

(a) 3 (b) 4.3 (c) 2.9 (d) None of these

35. In Question 34, what is the value of F(x) at x=2.3

(a) 6.2 (b) 7.3 (c) 6.9 (d) None of these

36. 35. In Question 34, what is the value of F(x) at x=0

(a) 1 (b) 2 (c) 3 (d) None of these

37. For getting the solution of non-linear equation, which method uses the tangent


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(a) Bisection (b) Iterative (c) Newton Raphson (d) Regula Falsi

38. Jordan method is a refinement over Gausees method

(a) True (b) False (c) Cant say

39. Numerical Solutions always give accurate solution(a) True (b) False

40. What will be the relative error if 2/3 is approximated to 0.667?

(a) 0.0005 (b) 0.0006 (c) 0.005 (d) None

Computer Oriented Numerical Analysis Assignment

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