matlab accuracy in linear functions

Hello fellows,

help me understand Matlab accuracy. I try modeling simple “zick-zack” signal:

      x=0:dt:4;
      slope=0.1;    

      h=(numel(x)-1)/4;
      y(1:h+1)=x(1:h+1)*slope;
      y(h+2:3*h+1)=2*y(h+1)-(x(h+2:3*h+1)*slope);
      y(3*h+2:4*h+1)=4*y(3*h+1)+(x(3*h+2:4*h+1)*slope);

and the last entry of y results to be -1,11022302462516e-16. I understand that there is a limit of accuracy but why here? Can you explain it for me or point my mistake

P.S:

In the end I change script to:

      y(1:h+1)=x(1:h+1)*slope;
      y(h+2:3*h+1)=2*y(h+1)-(x(h+2:3*h+1)*slope);
      y(3*h+2:4*h+1)=y(2:h+1)-0.1;

and now I can search for all x=0 entries

Answer 1

[Walter Roberson]

http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F