3. (B) Program for Newton’s backward interpolation.

3. (B) Program for Newton’s backward interpolation.

	clc;clear;close x=[15 20 25 30 35 40];
	y=[0.2588190 0.3420201 0.4226183 0.5 0.5735764 0.6427876];
	h=5
	c=1;
	for i=1:5
	d1(c)=y(i+1)-y(i);
	c=c+1;
	end
	c=1;
	for i=1:4
	d2(c)=d1(i+1)-d1(i);
	c=c+1
	end
	c=1;
	for i=1:3
	d3(c)=d2(i+1)-d2(i);
	c=c+1;
	end
	c=1;
	for i=1:2
	d4(c)=d3(i+1)-d3(i);
	c=c+1;
	end
	c=1;
	for i=1:1
	d5(c)=d4(i+1)-d4(i);
	c=c+1 ;
	end
	d=[d1(5) d2(4) d3(3) d2(2) d1(1)];
	x0=38;
	pp=1;
	y_x=y(6);
	p=(x0-x(6))/h;
	for i=1:5
	pp=1;
	for j=1:i
	pp=pp*(p-(j-1))
	end
	y_x=y_x+(pp*d(i))/factorial(i);
	end
	printf('value of function at %f is:%f',x0,y_x);