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+//error in lagrange's interpolation formula

+//example 3.18

+//page 107

+clc;clear;close;

+x=[2 2.5 3.0];

+y=[0.69315 0.91629 1.09861];

+deff('y=l0(x)','y=(x-2.5)*(x-3.0)/(-0.5)*(-1.0)')

+x=poly(0,'x');

+disp(l0(x),'l0(x)=');

+deff('y=l1(x)','y=((x-2.0)*(x-3.0))/((0.5)*(-0.5))')

+x=poly(0,'x');

+disp(l1(x),'l1(x)=');

+deff('y=l2(x)','y=((x-2.0)*(x-2.5))/((1.0)*(0.5))')

+x=poly(0,'x');

+disp(l2(x),'l2(x)=');

+f_x=l0(2.7)*y(1)+l1(2.7)*y(2)+l2(2.7)*y(3);

+printf(' the calculated value is %f:',f_x);

+err=abs(f_x-log(2.7));

+deff('y=R_n(x)','y=(((x-2)*(x-2.5)*(x-3))/6)');

+est_err=abs(R_n(2.7)*(2/8))

+if est_err>err then

+    printf('\n\n the error agrees with the actual error')

+end
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