1. (25 pts) Given the following start for a Matlab function: function [answer] = NewtonForm(m,x,y,z) that inputs • number of data points m; • vectors x and y, both with m components, holding x- and y-coordinates, respectively, of data points; • location z; and uses divided difference tables and Newton form to output the value of the Lagrange polynomial, interpolating the data points, at z.
clear all
close all
%x and y values for finding the
%function for which interpolation have to do
func=@(x) 1./(1+25.*x.^2);
x1=linspace(-1,1,21);
y1=func(x1);
%all interpolating points
z1=linspace(-1,1,101);
%displaying the function
fprintf('The function is f(x)=\n')
disp(func)
%Function for Newton Divide difference
[Value]=NewtonForm(21,x1,y1,z1);
figure(1)
scatter(x1,y1,'filled','Linewidth',2)
hold on
plot(z1,Value,'r')
xlabel('x')
ylabel('f(x)')
title('x vs. f(x) plot')
legend('Actual data','Interpolating data')
%Function for Newton Divided difference interpolation
function [Value]=NewtonForm(m,x1,y1,z1)
%Creatin the Newton Divided difference formulae
for variable x
syms x
y2=y1;
zz=zeros(m,m+1);
zz(:,1)=x1'; zz(:,2)=y1';
for i=1:m-1
n1=length(y2);
for j=1:n1-1
y3(j)=(y2(j+1)-y2(j))/(x1(i+j)-x1(j));
zz(j,i+2)=y3(j);
end
z(i)=y3(1);
y2=y3;
clear y3;
end
nn=length(zz);
%loop for creating the function
n=length(z);
for i=1:n
s1=1;
for j=1:i
s1=(x-x1(j))*s1;
end
zz1(i)=(s1)*z(i);
end
f_newton(x)=sum(zz1)+y1(1);
Value=double(f_newton(z1));
end
%%%%%%%%%%%%%%% End of Code %%%%%%%%%%%%%%
1. (25 pts) Given the following start for a Matlab function: function [answer] = NewtonForm(m,x,y,z) that inputs • number of data points m; • vectors x and y, both with m components, holding x- and y-...
1. (25 pts) Write a Matlab function with the header function [value- polynomialpiece(m,x.y,k,z) that inputs number of data points m; vectors a and y, both with m components, holding r- and y-coordinates, respec- tively, of data points, and where the components of r are evenly spaced and in increasing order (rk/2,z,n+1-k/2) an even number k and a location distinct from the 0, > z . nodes; and outputs, using Lagrange form, the value at z of the deg S k-1...
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