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PAllen's latest activity
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PAllen
replied to the thread
I
Why fixed point iteration of ##x^3 = 1-x^2## doesn't converge when ##x_0= 0##
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Looking over the convergence proof in the book I referenced, it seems tweaking the argument can remove the need to prohibit g’ being...
Jul 20, 2025
P
PAllen
replied to the thread
I
Why fixed point iteration of ##x^3 = 1-x^2## doesn't converge when ##x_0= 0##
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The question was about convergence. For that, the requirement is the the derivative condition holding in a neighborhood of the root.
Jul 20, 2025
P
PAllen
replied to the thread
I
Why fixed point iteration of ##x^3 = 1-x^2## doesn't converge when ##x_0= 0##
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A sufficient contrition is different from a necessary condition.
Jul 20, 2025
P
PAllen
replied to the thread
I
Why fixed point iteration of ##x^3 = 1-x^2## doesn't converge when ##x_0= 0##
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Also, note that g’(x) greater than one near the root.
Jul 20, 2025
P
PAllen
replied to the thread
I
Why fixed point iteration of ##x^3 = 1-x^2## doesn't converge when ##x_0= 0##
.
The derivative can’t be zero at any guess. This is assumed in derivations of convergence of the method. It is also required that an...
Jul 20, 2025
P
PAllen
replied to the thread
I can no longer render LaTeX
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Can you clarify? I see you would never want to use a posted insight; that's why I suggested a dummy (draft) insight. Once the latex...
Jul 14, 2025
P
PAllen
replied to the thread
I can no longer render LaTeX
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One other possible workaround is to keep a dummy insight around. Latex preview in Wordpress works just fine. When done, cut and paste to...
Jul 14, 2025
P
PAllen
replied to the thread
Latex help page not rendering
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θ What other alternative is there? The $$ and ## is the only thing I have ever used! Are there any instructions for the alternative...
Jul 10, 2025
P
PAllen
replied to the thread
At what age is special relativity taught?
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Well I think a first course in EM should use SR, and this was done already circa 1970 in many US colleges - including the very intro EM...
Jul 8, 2025
P
PAllen
replied to the thread
A
Weyl tensor and coordinate acceleration
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I think this might be the Nordtvedt article being refernenced. I have no idea if there is a free version of this paper. It is not...
Jul 7, 2025
P
PAllen
replied to the thread
A
Weyl tensor and coordinate acceleration
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A discussion of the absence of the Nordtvedt effect in GR can be found in section 4.3.1 of...
Jul 7, 2025
P
PAllen
posted the thread
Latex help page not rendering
in
Feedback and Announcements
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For me, at the moment, the latex help page is not rendering. No number of refreshes fixes it. Also, at this moment, preview in replies...
Jul 6, 2025
P
PAllen
replied to the thread
A
Photon decay/splitting
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Here is an old thread I started, addressing this very question. The discussion turned up a bunch of historic literature on the subject...
Jul 2, 2025
P
PAllen
replied to the thread
A
Understanding the Gravitational Redshift Caused by a Black Hole
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Your scenario of a growing BH is needlessly complex. Consider, instead, two raindrop observers, one just ahead of the other. The outer...
Jun 24, 2025
P
PAllen
replied to the thread
A
Understanding the Gravitational Redshift Caused by a Black Hole
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Since there is no special class of hovering observers, you need to take account of the motion of the emitter and receiver. Then the...
Jun 24, 2025
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