NUMERICAL ANALYSIS WEEK 6 2015

CURVE FITTING

 

PROBLEM 1

Fit a linear line by using polynomial least square curve fitting

X

2

3

4

7

8

9

5

5

Y

9

6

5

10

9

11

2

3

 

PROBLEM 2

X

y

0

-2.20

0.1

-1.90

0.2

0

0.3

-0.1

0.4

-0.01

0.5

-0.3

0.6

-0.2

0.7

-0.09

0.8

0.4

0.9

-0.1

1.0

-1.1

1.1

-1.3

1.2

-2

1.3

-1.8

1.4

-0.02

1.5

1

Data in the above table is given

a)      Fit a polynomial least square curve

b)     Use interpolation polynomials to fit the data

 

PROBLEM3

 

X

y

0

0

1

1

2

4

3

8

Fit cubic spline to the data.

 

 PROBLEM 4

Liquid flows through a sphere. Friction drag coefficient CD is given as a function of Reynolds number. Fit a cubic spline interpolation polynomial to the data. Find CD values for Re = 5, 50, 500 and 5000 .

Note: Logarithmic scale can be used.

 

Re

0.2

 

2

20

200

2000

20 000

CD

103

 

13.9

2.72

0.800

0.401

0.433

 

  PROBLEM 5

Solve problem 4 by using 4 point Lagrange and Newton interpolation formula

 

PROBLEM 6

Distance required to stop a car is function of velocty. This relation is given in the table below

Velocity (km/h)

24

32

40

48

Stopping distance (m)

4.8

6.0

10

12

If the vehicle travels with a velocity of 38 km/h, calculate stopping distance by using Newton interpolation formula.