newton.m

X1=[-.5 -.4111 -.3222 -.2333 -.1444 -.0556 0.0333 .1222 .2111 .3 .3889 .4778 .5667 .6556 .7444 .8333 .9222 1.0111 1.1];
Y1=[-1.8791161 -1.4863026 -1.2340791 -1.0889126 -1.0210957 -1.0012003 -.9997404 -.9872194 -.9341338 -.08109635 -.5884439 -.2398145 0.2504693 0.8644380 1.5092225 1.9638191 1.8573017 0.8153058 -.08237622];
xr=[-0.4556 -0.2778 -0.1444 0.0333 0.2111 0.3889 0.6111 0.7889 0.9667 1.1444];
yr=[-1.6626043 -1.1499897 -1.0210957 -.9997407 -.9341338 -.5884439 0.5454266 1.7803107 1.4644281 -1.0369071];
plot(X1,Y1,'b*');
number=19;
for count=1:1:18
    diff=round(18/count);
    %disp(diff);
    j=1;
    % i=0;
    x=zeros(1,19);
    y=zeros(1,19);
    for i=1:diff:19


        x(1,j)= X1(1,i);
        y(1,j)=Y1(1,i);
        j=j+1;
        %i=i+diff;

    end
    if(x(1,j-1)~=X1(1,19))

        x(1,j)=X1(1,19);
        y(1,j)=Y1(1,19);


    else
        j=j-1;
    end
    disp(x);
    length=j;

    ar(1:length,1) = x(1,1:length);
    ar(1:length,2) = y(1,1:length);


    for a = 1:length-1
        for b = 1:length-a
            ar(b,a+2) = (ar(b+1,a+1)-ar(b,a+1))/(ar(b+a,1)-ar(b,1));
        end
    end

    xv(1,1:length)=x(1,1:length);
    yv(1,1:length)=y(1,1:length);
    mul = zeros(length-1,length);
    p = conv(1,[1,-xv(1)]);

    for c = 1:length-1
        mul(c,(length-c):length) = ar(1,c+2).*p;
        p = conv(p,[1,-x(c+1)]);
    end

    P = sum(mul,1);
    P(1,length)=P(1,length)+y(1);


    x_eval = -.5:0.1:1.1;
    y_eval = polyval(P,x_eval);
    plot(x_eval,y_eval);
    hold on;
    plot(xr,yr,'b*');
    hold on;
    pause(1);
    hold off;


end

clear ;