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List:       kde-edu-devel
Subject:    D24972: Keep cumulated error negligible for rapidly increasing functions
From:       Yuri Chornoivan <noreply () phabricator ! kde ! org>
Date:       2019-11-23 13:07:38
Message-ID: 4f6fea0a21ae4e7e949cce505afc2068 () localhost ! localdomain
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yurchor added a comment.


  Just some considerations:
  
  1. dx ~ (x_max-x_min)/viewport_width (about 0.001 for relatively low values of x).
  2. Error for Simpson's rule (Runge-Kutta method degrades to this rule in case of \
y'(x)=f(x) integration) is f^(4)(\xi)*dx^5/2880.  3. To have cumulative error less \
than 1 for a viewport width 1000 it is enough to satisfy f^(4)(\xi)*dx^5/2880 < \
0.001.  4. If f^(4)(x) is of dy/dx^4 order so it is enough to multiply it with dx^2 \
to approximately satisfy 3. under the above-mentioned conditions.

REPOSITORY
  R334 KmPlot

REVISION DETAIL
  https://phabricator.kde.org/D24972

To: yurchor, #kde_edu
Cc: aacid, cfeck, kde-edu, narvaez, apol


[Attachment #3 (text/html)]

<table><tr><td style="">yurchor added a comment.
</td><a style="text-decoration: none; padding: 4px 8px; margin: 0 8px 8px; float: \
right; color: #464C5C; font-weight: bold; border-radius: 3px; background-color: \
#F7F7F9; background-image: linear-gradient(to bottom,#fff,#f1f0f1); display: \
inline-block; border: 1px solid rgba(71,87,120,.2);" \
href="https://phabricator.kde.org/D24972">View Revision</a></tr></table><br \
/><div><div><p>Just some considerations:</p>

<ol class="remarkup-list">
<li class="remarkup-list-item">dx ~ (x_max-x_min)/viewport_width (about 0.001 for \
relatively low values of x).</li> <li class="remarkup-list-item">Error for \
Simpson&#039;s rule (Runge-Kutta method degrades to this rule in case of \
y&#039;(x)=f(x) integration) is f^(4)(\xi)*dx^5/2880.</li> <li \
class="remarkup-list-item">To have cumulative error less than 1 for a viewport width \
1000 it is enough to satisfy f^(4)(\xi)*dx^5/2880 &lt; 0.001.</li> <li \
class="remarkup-list-item">If f^(4)(x) is of dy/dx^4 order so it is enough to \
multiply it with dx^2 to approximately satisfy 3. under the above-mentioned \
conditions.</li> </ol></div></div><br \
/><div><strong>REPOSITORY</strong><div><div>R334 KmPlot</div></div></div><br \
/><div><strong>REVISION DETAIL</strong><div><a \
href="https://phabricator.kde.org/D24972">https://phabricator.kde.org/D24972</a></div></div><br \
/><div><strong>To: </strong>yurchor, KDE Edu<br /><strong>Cc: </strong>aacid, cfeck, \
kde-edu, narvaez, apol<br /></div>



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