Lesfip scales: Difference between revisions
Wikispaces>genewardsmith **Imported revision 192238344 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 192264102 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-01-10 14: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-01-10 16:14:15 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>192264102</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">A //lesfip scale// (LEast Squares FIxed Point) is a scale which for some range of values for error tolerance, is a fixed point for the least squares algorithm minimizing the sum of squared error relative to some target list of intervals. That is, when we minimize the sum of the squares of all of the errors less than some fixed value such as seven cents, we obtain the same scale back again.</pre></div> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">A //lesfip scale// (LEast Squares FIxed Point) is a scale which for some range of values for error tolerance, is a fixed point for the [[http://en.wikipedia.org/wiki/Least_squares|least squares algorithm]] minimizing the sum of squared error relative to some target list of intervals. That is, when we minimize the sum of the squares of all of the errors less than some fixed value such as seven cents, we obtain the same scale back again. | ||
A lesfip scale may be found by choosing a [[periodic scale|scale]], a target set of intervals, an an error tolerance. The least squares optimization is iterated until a fixed point is arrived at. Occasionally there may be a problem when the system becomes underdetermined, which can be fixed by increasing the error tolerance by some amount for one iteration.</pre></div> | |||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Lesfip scales</title></head><body>A <em>lesfip scale</em> (LEast Squares FIxed Point) is a scale which for some range of values for error tolerance, is a fixed point for the least squares algorithm minimizing the sum of squared error relative to some target list of intervals. That is, when we minimize the sum of the squares of all of the errors less than some fixed value such as seven cents, we obtain the same scale back again.</body></html></pre></div> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Lesfip scales</title></head><body>A <em>lesfip scale</em> (LEast Squares FIxed Point) is a scale which for some range of values for error tolerance, is a fixed point for the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Least_squares" rel="nofollow">least squares algorithm</a> minimizing the sum of squared error relative to some target list of intervals. That is, when we minimize the sum of the squares of all of the errors less than some fixed value such as seven cents, we obtain the same scale back again.<br /> | ||
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A lesfip scale may be found by choosing a <a class="wiki_link" href="/periodic%20scale">scale</a>, a target set of intervals, an an error tolerance. The least squares optimization is iterated until a fixed point is arrived at. Occasionally there may be a problem when the system becomes underdetermined, which can be fixed by increasing the error tolerance by some amount for one iteration.</body></html></pre></div> | |||