Question

1. (25 pts) Given integer N>0; vector x of distinct nodes with N components; vector y of valucs at nodes with N components; location 2 complete the Matlab function with header function [valuelagrangeforminterpolation(N,x,yz) so that it uses the Lagrange form to output the value of the Lagrange interpolating polynomial at Remember Lagrange form:

Answer 1

Matlab example for Lagrange Interpolation function clear all close all %Example and y for using function p-polyintour as tname(x,y,w) data values x1-1 2 4 5.5 7.5910; yl--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,xl,yl,w); hold on %plotting of interpolated data plot (w,p) title( 'Data plotting using Lagrange Interpolation') xlabel ("х value. ) ylabel('Y value legend('Actual Data, Interpolated data') 8 88888888888883888888888888888 8888888888888888888888 %%%% % % % % % % Matlab function for Lagrange interpolation function [value]-lagrangeforminterpolation (N,x,y, 2) %888888%88 syms xx #xi-independent variable ;yi-dependent variable ; x-value which at we have to find the dependent variable ;y-Corresponding value of dependent variable at x #100p for creating the Lagrange Interpolation function for i- 1: N s1-1; s2-l for j-1:N if i--j s1-(xx-x ( j ) ) *s1; end end end f (xx)-sum ( zz) tinterpolated data using Lagrange Method for i= 1:length(z) value(i)-double(f(z(i))); end end 옹옹88888888888888888888888888898888888888888888踐88888888888888 888888 용음음%용음음%용욤욤응용음 End of Code 욤욤욤욤욤욤응응용욤응응용욤

Data plotting using Lagrange Interpolation 700 -Actual Data ated data 600 500 400 300 100 1 23456789 10 X value Published with MATLAB R2018a

%%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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