COMP 350 Study Guide - Midterm Guide: Gaussian Elimination, Triangular Matrix, Taylor Series

• School: McGill University
• Department: Computer Science (Sci)
• Course: COMP 350
• Professor: Xiao- Wen Chang

Document Summary

Comp 350 midterm review: ieee floating point systems. Definition of e - upper bound on the relative error due to rounding in floating point arithmetic. The gap between the number 1 and the next larger oating point number is called the machine epsilon of the oating point system, denoted by e. Format of single and double floating point number. The number can"t be normalized since that would result in an exponent which does not fit in the field. We are given a number: what is the floating point number that comes right after/before that number. Since we can deduce it from the exponent we add an additional bit for precision. Prove: | round(x) - x | : < eps * 2^e (any mode) or <= 0. 5 eps * 2^e (to nearest) If nmin<=|x|<=nmax then | (round(x)-x)/x | < eps (any node) or <= 0. 5 eps (to nearest) (make sure you know how to prove this)