[Maxima-bugs] [ maxima-Bugs-1663536 ] newton sometines very slow

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Bugs item #1663536, was opened at 2007-02-19 08:50
Message generated for change (Comment added) made by willisbl
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Category: None
Group: None
>Status: Closed
>Resolution: Invalid
Priority: 5
Private: No
Submitted By: Barton Willis (willisbl)
Assigned to: Nobody/Anonymous (nobody)
Summary: newton sometines very slow

Initial Comment:
Fast:

(%i19) newton(x^2 - %i, 1 - %i/5);
(%o19) 7.071067853080116b-1*%i+7.071067813155526b-1

So slow I don't know that it ever finishes:

(%i20) newton(x^2 - %i, 1 - %i);

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>Comment By: Barton Willis (willisbl)
Date: 2007-02-22 05:24

Message:
Logged In: YES 
user_id=895922
Originator: YES

You are correct. I was confused. 

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Comment By: Raymond Toy (rtoy)
Date: 2007-02-20 10:19

Message:
Logged In: YES 
user_id=28849
Originator: NO

Is newton required to converge from this starting point?

I modified newton to print out each guess.  It looks like newton is stuck,
and keeps moving back and forth on some line, constantly producing guesses
of the form a-a*%i.  Plugging this into the newton iteration shows that the
next guess would be (1-%i)*(2*a^2-1)/(4*a), so the form of the next answer
never changes.

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