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Given the relative condition number of a root x = r of ax? + bx + c=0 due to perturbations in a: K = |r/(r1 – r2)| where ri and r2 are two roots of the equation. Find the relative error in computing the two roots f (a) = r where a = 1.002 and fl(a) = 1.001. Show the relative error is roughly smaller than the condition number times the relative error in a, assuming no round-off error in the computation: ax? + 2.002x +1=0

Given the relative condition number of a root x = r of ax? + bx + c=0 due to perturbations in a: K = |r/(r1 – r2)| where ri and r2 are two roots of the equation. Find the relative error in computing the two roots f (a) = r where a = 1.002 and fl(a) = 1.001. Show the relative error is roughly smaller than the condition number times the relative error in a, assuming no round-off error in the computation: ax? + 2.002x +1=0

Advanced Engineering Mathematics
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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Given the relative condition number of a root x = r of ax? + bx + c=0 due to perturbations in a: K = |r/(r1 – r2)| where ri and r2 are two roots of the equation. Find the relative error in computing the two roots f (a) = r where a = 1.002 and fl(a) = 1.001. Show the relative error is roughly smaller than the condition number times the relative error in a, assuming no round-off error in the computation: ax? + 2.002x +1=0
Transcribed Image Text:Given the relative condition number of a root x = r of ax? + bx + c=0 due to perturbations in a: K = |r/(r1 – r2)| where ri and r2 are two roots of the equation. Find the relative error in computing the two roots f (a) = r where a = 1.002 and fl(a) = 1.001. Show the relative error is roughly smaller than the condition number times the relative error in a, assuming no round-off error in the computation: ax? + 2.002x +1=0
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