3. ( 8 marks) Floating Point Error Analysis Show that if x,y,z are already floating point numbers in
some floating point system F, the relative error of the floating point calculation (xy)z with respect to
the true value of (xy)/z is less than or equal to 2E+E2 (where E is machine epsilon for the FP
system F ) assuming no overflow/underflow errors occurs. The symbols and here represent
floating point subtraction and division, respectively. Just like we saw for addition in class, they
satisfy ab=fl(ab) and ab=fl(a/b), for floating point inputs a and b..
3 8 marks Floating Point Error Analysis Show that if xy.pdf
1. 3. ( 8 marks) Floating Point Error Analysis Show that if x,y,z are already floating point numbers in
some floating point system F, the relative error of the floating point calculation (xy)z with respect to
the true value of (xy)/z is less than or equal to 2E+E2 (where E is machine epsilon for the FP
system F ) assuming no overflow/underflow errors occurs. The symbols and here represent
floating point subtraction and division, respectively. Just like we saw for addition in class, they
satisfy ab=fl(ab) and ab=fl(a/b), for floating point inputs a and b.
