AI Tutor
Back to Accuracy of Computations

Exercise 4

Avg difficulty 3.0

Rounding inside the computer often has an effect on the result. Assume that your machine has eight significant digits.

  • Show that the machine will compute (2/3)+((2/3)−(1/3))(2/3)+((2/3)-(1/3)) as unequal to ((2/3)+(2/3))−(1/3)((2/3)+(2/3))-(1/3). Thus, computer arithmetic is not associative.

  • Compare the computer’s version of (1/3)x+y=0(1/3)x+y=0 and (2/3)x+2y=0(2/3)x+2y=0. Is twice the first equation the same as the second?

Hefferon, Linear Algebra, Linear Systems, Accuracy of Computations, Exercise 4

AI Tutor

Adapted from Linear Algebra © 2016 Jim Hefferon. Licensed under CC BY-SA 3.0 US. Source: Linear Algebra. Imported at revision df2262e.