Révision 69 pobysoPythonSage/src/sageSLZ/sageSLZ-Notes.html

sageSLZ-Notes.html (revision 69)
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<p>The naive approach is to:</p>
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<ol>
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  <li>give it a try with the initial data;</li>
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  <li>you get a too large error, reduce (e. g. divide by 2) the interval by
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    lowering the upper bound until the computed error matches the expected
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  <li>when you get a too large error, reduce (e. g. divide by 2) the interval by
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    lowering the upper bound until the computed error matches the target
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    error;</li>
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  <li>use this upper bound as the lower bound of the next interval, always
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  <li>this upper bound becomes the lower bound of the next interval, always
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    using the orginal upper bound and repeat the process until you can cover
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    the all initial interval with the computed sub-interval.</li>
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</ol>
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<p>In step 2 you may have to compute several polynomials until the computed


  		





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error is below or equal to the expected error. You must not decrease the


  		





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interval width too agressively since it multiplies the number of interval (and


  		





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lengtens the subsequent manipulations that are made on each sub-interval).</p>


  		





  
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interval width too agressively.  There is no point in getting a too small approximation error since it multiplies the number of interval (and


  		





  
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lengthens the subsequent manipulations that are made on each sub-interval).</p>


  		





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<p>In step 3 you probably unutily compute polynomials for too large interval


  		





  
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<p>In step 3 you probably inutily compute polynomials for too large intervals


  		





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and you could know it from the previous computations.</p>


  		





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<p>The whole idea is to reduce the number of polynomila computation and get the


  		





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maximum width (compatibile with the expected approwimaiton error).</p>


  		





  
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<p>The whole idea is to reduce the number of polynomial computations and get the


  		





  
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maximum width (compatible with the expected approwimaiton error).</p>


  		





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<p>This process has different aspects:</p>


  		





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<ol>


  		





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<p>For point 2, can some type of data structure keep the informations (which


  		





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ones ?) and allow for an efficient reuse.</p>


  		





  
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<p>Adjacent question: is it possible, given a the result of a previous


  		





  
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computation, to forecast the effect on the approximation precision of a degree


  		





  
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in(de)crease?</p>


  		





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</body>


  		





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</html>


  		












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