Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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When f=C¹ (R,R), and X*ER is a point with f(x*)=0 and f'(x*) ±0, then we know that there exists
some 8>0 such that for every xBg(x*), the parallel chord method converges to x*. What is
the deeper reason why this is true?
(You should know this reason, and you are simply asked to recognise it, so there is no need
for proofs or counterexamples in this question.)
a. For sufficiently small 8>0, the parallel chord method g(x)=x-f(x)/f'(x。) is a contraction
on B8(x*).
O b. For sufficiently small 8>0 the parallel chord method g(x)=x-f(x)/f'(x。) is a contraction
from R into Bg(x*), i.e. for every XER, there exists N≥0 such that g(x)=Bs(x*) for all
k₂N.
O c.
I think that my friend thinks that the tutor thinks that the lecturer thinks that this
statement is true. So my lecturer thinks that my tutor thinks that my friend thinks
that I should tick this box. So this must be the box to tick.
Od. The parallel chord method g(x)=x-f(x)/f'(x。) has the Newton property.
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Transcribed Image Text:When f=C¹ (R,R), and X*ER is a point with f(x*)=0 and f'(x*) ±0, then we know that there exists some 8>0 such that for every xBg(x*), the parallel chord method converges to x*. What is the deeper reason why this is true? (You should know this reason, and you are simply asked to recognise it, so there is no need for proofs or counterexamples in this question.) a. For sufficiently small 8>0, the parallel chord method g(x)=x-f(x)/f'(x。) is a contraction on B8(x*). O b. For sufficiently small 8>0 the parallel chord method g(x)=x-f(x)/f'(x。) is a contraction from R into Bg(x*), i.e. for every XER, there exists N≥0 such that g(x)=Bs(x*) for all k₂N. O c. I think that my friend thinks that the tutor thinks that the lecturer thinks that this statement is true. So my lecturer thinks that my tutor thinks that my friend thinks that I should tick this box. So this must be the box to tick. Od. The parallel chord method g(x)=x-f(x)/f'(x。) has the Newton property.
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