Question

Problem 5 (programming): Create a MATLAB function named lagrange interp.m to perform interpolation using Lagrange polynomials. Download the template for function lagrange interp.m. The tem Plate is in homework 4 folder utl TritonED·TIue function lakes in the data al nodex.xi and yi, as well as the target x value. The function returns the interpolated value y. Here, xi and yi are vectors while x and y are scalars. You are not required to follow the template; you can create the function in your way The formula for Lagrange interpolation is given as follows: where n is the degree of the polynomials and L ) are cardinal functions defined as follows: )=0 )礼 Use function lagrange İnterp.m and the seawater ternperature data in table 1 to perform (a) Estimate the temperature at depth z150 m using nodes 3 through 5. Put the (b) Estimate the temperature at depth z-150 m using nodes 3 through 6. Put the (c) Estimate the temperature at depth z-150 m using al nodes. Put the answer in (d) Create a vector depth -330:10:-10. Estimate the temperature for every element the following exercises. answer in p5a answer in p5b p5c in vector depth and store them in vector temperature. Use all nodes to perform the interpolation. Make a figure 5, e.g. figure(5). Use a solid line to plot temperature versus depth with depth on the y-axis and temperature on the x axis. Also, use symbols to plot all nodes on table 1. Remember to give the figure a legend and a title and label the axes. Set p5d"See figure 5' (e) Based on the figure, comment on the accuracy of the interpolation. Give the answer as p5e '...'. Keep in mind the fact that warm water is lighter than cold water

Answer 1

`Hey,

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clc%clears the screen
clear all %clears the history
format long;
x=input('Enter x vector(depth) from table as mentioned in question: ');
y=input('Enter x vector(temp) from table as mentioned in question: ');
p5a=lagrange_interp(x(3:5),y(3:5),-150)
p5b=lagrange_interp(x(3:6),y(3:6),-150)
p5c=lagrange_interp(x,y,-150)
depth=-330:10:-10;
temp=lagrange_interp(x(3:5),y(3:5),depth)
figure(5);
plot(temp,depth,x,y,'o');
p5d='See figure 5';

function [yhat]=lagrange_interp(x,y,interpx)

X=x;
f=y;
x=interpx;

l=0;
for i=1:length(X)
li=1;
for j=1:length(X)
if i~=j
li=(li).*((x-X(j))/(X(i)-X(j)));
end
end
l=(l)+((li)*f(i));
end
yhat=l;
  
end

Kindly revert for any queries

Thanks.