Question

1. (25 pts) Given integer N > 0; vector r of distinct nodes with N components, ordered from smallest to largest; vector y of nonzero values at nodes with N components suppose the piecewise linear interpolant P(x) of this data has a root. Complete the Matlab function with header function [root] linearinterpolationroot(N,x.y) so that it outputs the smallest root of P(r). Remember, the piecewise linear interpolant is only defined between the smallest and largest nodes.

Answer 1

%%Matlab example for Lagrange Interpolation function
clear all
close all
%Example for using function p=polyintourastname(x,y,w)
%x and y data values
x1=[1 2 4 5.5 7.5 9 10];
y1=[-6.5 -18.5 -26.5 14 184.5 436.5 679];
%plotting of actual data
plot(x1,y1);
%interpolated data points
w=linspace(1,10,200);
p=lagrangeforminterpolation(7,x1,y1,w);
hold on
%plotting of interpolated data
plot(w,p)
title('Data plotting using Lagrange Interpolation')
xlabel('X value')
ylabel('Y value')
legend('Actual Data','Interpolated data')

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%%%%%%%%%% Matlab function for Lagrange interpolation %%%%%%%%%%
function [value]=lagrangeforminterpolation(N,x,y,z)
syms xx
%xi=independent variable;yi=dependent variable;x=value at which we have to
%find the dependent variable;y=corresponding value of dependent variable at x;
%loop for creating the Lagrange Interpolation function
for i=1:N
s1=1;
s2=1;
for j=1:N
if i~=j
s1=(xx-x(j))*s1;
s2=(x(i)-x(j))*s2;
end
end
zz(i)=(s1./s2)*y(i);
end
f(xx)=sum(zz);
%interpolated data using Lagrange Method
for i=1:length(z)
value(i)=double(f(z(i)));
end

end

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%%%%%%%%%%%%%% End of Code %%%%%%%%%%%%%%

Data plotting using Lagrange Interpolation 700 Actual Data Interpolated data 600 500 400 300 200 100 -100 10 5 K value Published with MATLAB R2018a 2