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RE: For a variety of plotting experiences, maybe bugs? (small intervals)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg124114] RE: [mg124074] For a variety of plotting experiences, maybe bugs? (small intervals)
  • From: "David Park" <djmpark at comcast.net>
  • Date: Mon, 9 Jan 2012 03:20:17 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <je3vti$eeh$1@smc.vnet.net> <je6e5h$q7b$1@smc.vnet.net> <24475751.93762.1326015447306.JavaMail.root@m06>

Small domains and small intervals are often treated masochistically. And why
the powers of 2 instead of 10? 

This is the easy way to make the plots. Use a reasonable domain and range
and enough WorkingPrecision.

With[{n = 140},
 Plot[(Cos[x 10^-n + 1] - Cos[1]) 10^n, {x, 0, 1}, 
  WorkingPrecision -> n + 3,
  Frame -> True,
  FrameLabel -> {(y - 1) 10.^n, 10.^n (Cos[y] - Cos[1])}]
 ] 

Or use a series expansion:

Series[10^n (Cos[1 + x 10^-n] - Cos[1]), {x, 0, 2}] // Normal 

-2^(-1 - n) 5^-n x^2 Cos[1] - x Sin[1] 

and then use MachinePrecision:

With[{n = 145},
 Plot[-2^(-1 - n) 5^-n x^2 Cos[1] - x Sin[1], {x, 0, 1},
  WorkingPrecision -> MachinePrecision,
  Frame -> True,
  FrameLabel -> {(y - 1) 10.^n, 10.^n (Cos[y] - Cos[1])}]
 ] 

That is the way they do it in technical journals all the time. 


David Park
djmpark at comcast.net 
http://home.comcast.net/~djmpark/index.html 






From: Richard Fateman [mailto:fateman at cs.berkeley.edu] 


try this (I did it on version 7...)
>

Table[Plot[Cos[x], {x, 1 , 1 + 2.0^-i}], {i, 40, 45}]




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