Question

Write a complete set of Matlab instructions that implements cubic spline interpolation on the following data (assume clamped-end-condition). Your code should: a. Generate a single plot, over the range 0<= x <= 5, displaying: i. the individual data points ii. the generated spline function b. Predict the interpolated value at x = 0.5, x = 0.8 and x = 3.7 X у 0 1.7 1 0.3 2 1.8 3 0.4 4 2

Answer 1

Inorder to calculate the spline interpolation for the given data we can use matlab's interp1 fucntion.

interp1 takes 4 arguments:

1.) x: given x data

2.) y: given y data

3.) xv: range of x to interpolated for. here it is 0 to 5

4.) mode: mode of interpolation. here it is 'spline'

it returns a row vector yv, which contains y values for given xv values

plot x vs y and xv vs yv

program:

x = [0 1 2 3 4 ];

y = [1.7 0.3 1.8 0.4 2];

xv = 0:5;

yv = interp1(x,y,xv,'spline');

plot(x,y,'o',xv,yv,'-.')

output plot:

2.)

• The same process in the previous question can be used here to find x at 0.5, 0.8 and 3.7
• In the place of xv argument in interp1() , pass the given values of x.
• Also, the below program is a continualtion of program in previous question

​​​​​​​program:

y5 = interp1(x,y,0.5,'spline')

y8 = interp1(x,y,0.8,'spline')

y37 = interp1(x,y,3.7,'spline')

outputs:

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