Quiz Questions on Numerical Analysis and Floating-Point Arithmetic - Prof. Michael T. Heat, Quizzes of Mathematical Methods for Numerical Analysis and Optimization

Download Quiz Questions on Numerical Analysis and Floating-Point Arithmetic - Prof. Michael T. Heat and more Quizzes Mathematical Methods for Numerical Analysis and Optimization in PDF only on Docsity! Quiz 1: Clearly circle/box your answer. Name: Closed note, closed book, closed neighbor. 1. Why is it a bad idea to use an unstable algorithm? (a) It worsens the condition number of the given underlying problem. (b) It solves a nearby problem instead of the given problem. (c) It amplifies data error. (d) It amplifies computational error. 2. The infinite series 1 1− x = 1 + x+ x2 + . . . , is valid for all |x| < 1. To approximate 1/(1 − x) using only addition, one could truncate this series after the second term, obtaining 1 1− x ≈ 1 + x. What is magnitude of the absolute backward error from using 1 + x when x = 1/2? (a) 1/6 (b) 1/3 (c) 1/2 (d) 3/2 3. In normalized IEEE double-precision arithmetic, what operation on two positive floating-point numbers could result in underflow? (a) addition, subtraction, multiplication and division (b) subtraction, multiplication and division (c) subtraction and division (d) division 4. Consider the following mathematically equivalent expressions: (i) 1 x (1 + x) , (ii) 1 x − 1 1 + x , (iii) 1 1 + x ( 1 + x x − 1 ) . Which is most accurate in IEEE double-precision arithmetic when |x| is large (e.g., |x| > −1mach) ? (a) Expression (i) is most accurate. (b) Expression (ii) is most accurate. (c) Expression (iii) is most accurate. (d) All three are equally accurate.