Find the condition number at the root r = 1. Show that the forward error is roughly bounded by the backward error times the condition num- ber. (1) f(x) = x° – x = 0, r = 1, re = 1.1. (2) f(x) = x³ – 2x° + x = 0, r= 1. 3 -

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter7: Integration
Section7.1: Antiderivatives
Problem 45E
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Find the condition number at the root r
1.
Show that the forward error is roughly bounded
by the backward error times the condition num-
ber.
(1) f(x) = x° – x = 0, r = 1, re = 1.1.
(2) f(x) = x° – 2x° + x = 0, r = 1.
|
%3D
Transcribed Image Text:Find the condition number at the root r 1. Show that the forward error is roughly bounded by the backward error times the condition num- ber. (1) f(x) = x° – x = 0, r = 1, re = 1.1. (2) f(x) = x° – 2x° + x = 0, r = 1. | %3D
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