Numerical Analysis (ISS Statistics Paper I (Old Subjective Pattern)): Questions 14 - 21 of 21

Get 1 year subscription: Access detailed explanations (illustrated with images and videos) to 165 questions. Access all new questions we will add tracking exam-pattern and syllabus changes. View Sample Explanation or View Features.

Rs. 550.00 or

Question number: 14

» Numerical Analysis » Interpolation Formulae » Newton (Dividend Difference)

Appeared in Year: 2012

Essay Question▾

Describe in Detail

An unknown function u x has been tabulated below for some selected values of x. Use Newton’s divided difference formula on these to find an approximate value of u 3:

x

0

2

5

10

u x

3

19

73

223

Explanation

The Newton’s divided difference formula is used when the x-values not equally spaced. The Newton’s formula of divided difference for estimating u x corresponding to x is

Equation

where Equation, Equation, …

x

y

Equation

Equation

Equation

0

3

8

2

-0.05

2

19

18

1.5

-

5… (21 more words) …

Question number: 15

» Numerical Analysis » Summation Formula » Euler-Maclaurin's

Appeared in Year: 2013

Essay Question▾

Describe in Detail

Solve the equation:

Equation

Use Euler algorithm and tabulate the solution at x = 0.1, 0.2, 0.3.

Explanation

The given differential equation is

Equation

with initial condition x 0 = 0, y 0 = 0

Using Euler, s method,

Equation

where

Equation

We obtain y at x = 0.1

Equation

Equation

Equation

Again obtain y at x = 0.2

Equation

Equation

Equation

Similarly y at x = 0.3… (18 more words) …

Question number: 16

» Numerical Analysis » Interpolation Formulae » Lagrange

Appeared in Year: 2012

Essay Question▾

Describe in Detail

Solve the equation f (x) = 0 by using a suitable interpolation formula on the following values:

x

3

4

5

6

f (x)

-2.8

-1.2

-0.3

1.8

Explanation

To solve the equation f (x) = 0, using Lagrange’s inverse interpolation method

Equation

Equation

Equation

Equation

Equation

Question number: 17

» Numerical Analysis » Interpolation Formulae » Lagrange

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Fit the exponential curve y = a + bx to the following data

x: 0 2 4

y: 5.01 10 31.62

Explanation

his is not exponential equation, it is a straight line y = a + bx

S. no

x

y

Xy

x 2

1

0

5.01

0

0

2

2

10

20

4

3

4

31.62

126.48

16

Sum

6

46.63

146.48

20

The normal equations is

Equation

Equation

Using the… (33 more words) …

Question number: 18

» Numerical Analysis » Interpolation Formulae » Newton-Gregory

Appeared in Year: 2010

Essay Question▾

Describe in Detail

Evaluate log e 7 by Simpson’s -1/3rd rule.

Explanation

We get log e 7, when

Equation

So, the seven ordinates of the integrand using Simpson’s rule is

Equation

Where h = 1/6 (b-a) and y k =f (a + kh) for k = 1, 2, 3, 4, 5, 6, 7

Here, b = 7, a = 1, h =… (18 more words) …

Question number: 19

» Numerical Analysis » Interpolation Formulae » Newton-Gregory

Appeared in Year: 2010

Essay Question▾

Describe in Detail

Estimate U 2 from the following table:

x

1

2

3

4

5

U x

7

-

13

21

37

Explanation

To find the missing value, we use binomial expansion method. Here 4 values are known, we would take fourth order finite difference zero. Thus,

Equation

Equation

Equation

Here for x = 1, U 0 =7, U 1 =? , U 2 =13, U 3 =21, U 4 =37

Equation

Equation<span class="more">… (1 more words) …</span>

Question number: 20

» Numerical Analysis » Interpolation Formulae » Gauss

Appeared in Year: 2009

Essay Question▾

Describe in Detail

Find the value of

Equation

by taking 5 subintervals and using the Trapezoidal rule.

Explanation

Let Equation

First divided the interval into 5 subintervals

x

0

1/4

1/2

3/4

1

y

1

16/17

4/5

16/25

½

Here a = 0, b = 1, n = 4, h= (b-a) /n = 1/4

the Trapezoidal rule is

Equation

Equation

Equation

Equation

Question number: 21

» Numerical Analysis » Interpolation Formulae » Newton (Dividend Difference)

Appeared in Year: 2015

Essay Question▾

Describe in Detail

By making use of difference table and a suitable interpolation formula, find the number of student who obtained less than 45 marks in an examination, from the following table

Marks

30 - 40

40 - 50

50 - 60

60 - 70

70 - 80

Number of students

31

42

51

35

31

Explanation

Applying Newton-Gregory forward formula for interpolating the number of student who obtained less than 45 marks in an examination.

Marks less than

Number of student

Difference

∆y 0

2 y 0

3 y 0

4 y 0

x 0 =40

y 0 = 31

42

9

-25… (32 more words) …

f Page
Sign In