AMATH242 Study Guide - Quiz Guide: Secant Method, Radix Point, Approximation Error
15 Oct 2018
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Answer: floating point numbers may depart from their expected values in a way that the programmer cannot account for. Like we discussed in class today, one way to solve this problem is to de ne a small number e, for example e = 10 5, and evaluate the expression |x y| < e instead. Answer: in binary oating point systems, normalization gives us greater precision because we don"t need to store the bit following the radix point (another term for the. Decimal point) because we know it is always equal to 1. The expressions a2 b2 and a are similar in magnitude when a is large and b is small, so subtracting them is likely to give us a large relative error. To understand why, look up the condition number with respect to relative error for oating point addition (page.
