Question

interp1, polyfit, polyval, diff, trap, quad 1 INTERPOLATION (2 PTS) You did an experiment and obtained the following data set 90 x 10 20 30 60 70 80 100 60 82 111 140 167 198 200 220 Y 23 45 Create the x and y vectors to represent the above data and use the interpl command to find the interpolation result for the following questions 1. Use linear interpolation to approximate the value of y when x=15 2. Use cubic spline interpolation to approximate the value of y when x:15. 3. Use linear interpolation to approximate the value of x when y-80 4. Use cubic spline interpolation to approximate y-value for x-values evenly spaced between 10 and 100 at interval of 2. Plot the original data on an x-y plot as data points using "red circle" and the interpolated data using "blue dash line". 220 200 180 160 140 120 100 80 60 20 100 5. If you need to estimate the value outside of the observed range, you need to do extrapolation. You can use the same command by including options to get extrapotated value. Use help interp1 to find out how to estimate y when x-150 using "spline" method.

Answer 1

MATLAB Code:

close all
clear
clc

x = 10:10:100;
y = [23 45 60 82 111 140 167 198 200 220];

fprintf('Part 1\n---------------------------------------------------\n')
fprintf('Result: %f\n', interp1(x,y,15,'linear'))

fprintf('\nPart 2\n---------------------------------------------------\n')
fprintf('Result: %f\n', interp1(x,y,15,'spline'))

fprintf('\nPart 3\n---------------------------------------------------\n')
fprintf('Result: %f\n', interp1(y,x,80,'linear'))

xx = 10:2:100;
yy = interp1(x,y,xx,'spline');
plot(x,y,'ro',xx,yy,'b--')
xlabel('x'), ylabel('y')
legend('Data Points', 'Interpolated Curve', 'Location', 'northwest')
title('Part (4)')

Output:

Part 1
---------------------------------------------------
Result: 34.000000

Part 2
---------------------------------------------------
Result: 35.954676

Part 3
---------------------------------------------------
Result: 39.090909

Plot:

Part (4) 220 O Data Points 200 -_- Interpolated Curve 180 160 140 120 100 80 60 40 F 20叱 10 20 30 40506070 80 90 100