Problem 1: Consider the quantity a – b where a and b are real numbers. (a) Under what conditions should one expect an unusually large relative error in the computed value of a? – b? when this expression is evaluated in finite precision arithmetic? (b) Use 4-digit (decimal) rounding arithmetic to evaluate both a? – b² and (a+b)(a – b) with a = 995.1 and b = 995.0. Calculate the relative error in each result. (c) The expression (a + b)(a – b) is algebraically equivalent to a? – b², but it is a more accurate way to calculate this quantity if both a and b have exact floating point representations. Why?
Problem 1: Consider the quantity a – b where a and b are real numbers. (a) Under what conditions should one expect an unusually large relative error in the computed value of a? – b? when this expression is evaluated in finite precision arithmetic? (b) Use 4-digit (decimal) rounding arithmetic to evaluate both a? – b² and (a+b)(a – b) with a = 995.1 and b = 995.0. Calculate the relative error in each result. (c) The expression (a + b)(a – b) is algebraically equivalent to a? – b², but it is a more accurate way to calculate this quantity if both a and b have exact floating point representations. Why?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Problem 1: Consider the quantity a? – b? where a and b are real numbers.
(a) Under what conditions should one expect an unusually large relative error in the computed value
of a? – b? when this expression is evaluated in finite precision arithmetic?
(b) Use 4-digit (decimal) rounding arithmetic to evaluate both a? –b² and (a+b)(a-b) with a = 995.1
and b= 995.0. Calculate the relative error in each result.
(c) The expression (a + b)(a – b) is algebraically equivalent to a? – b², but it is a more accurate way
to calculate this quantity if both a and b have exact floating point representations. Why?
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