title: Fastest algorithm for computing the determinant of a matrix?
body: <p>For a research paper, I have been assigned to research the fastest algorithm for computing the determinant of a matrix.</p>
  
  <p>I already know about <strong>LU decomposition</strong> and <strong>Bareiss algorithm</strong> which both run in O(n^3), but after doing some digging, it seems there are some algorithms that run somewhere between n^2 and n^3. </p>
  
  <p>This <a href="http://books.google.com/books?id=7OqVdc2LGSUC&amp;pg=PA114&amp;lpg=PA114&amp;dq=coppersmith%20winograd%20algorithm%20for%20%22determinant%22&amp;source=bl&amp;ots=uRyJk7tG4G&amp;sig=jWx1yDmiRqF2TopdJyVFfe_2IWI&amp;hl=en&amp;sa=X&amp;ei=WKFrVOS6F4fToAT7yYGYAg&amp;ved=0CDwQ6AEwBDgK#v=onepage&amp;q=coppersmith%20winograd%20algorithm%20for%20%22determinant%22&amp;f=false" rel="noreferrer">source</a> (see page 113-114) and this <a href="http://books.google.com/books?id=S-tXjl1hsUYC&amp;pg=PA198&amp;lpg=PA198&amp;dq=coppersmith%20winograd%20algorithm%20for%20%22determinant%22&amp;source=bl&amp;ots=lEVtkf8Fr-&amp;sig=aovDprNRyU3aRSgSM15lIxLOu4k&amp;hl=en&amp;sa=X&amp;ei=nKFrVOTIJdHmoATPlIHoCg&amp;ved=0CD4Q6AEwBTgU#v=onepage&amp;q=coppersmith%20winograd%20algorithm%20for%20%22determinant%22&amp;f=false" rel="noreferrer">source</a> (see page 198) say that an algorithm exists that runs in O(n^2.376) because it is based on the Coppersmith-Winograd's algorithm for multiplying matrices. However, I have not been able to find any details on such an algorithm. </p>
  
  <p>My questions are:</p>
  
  <ol>
  <li>What is the fastest created (non-theoretical) algorithm for computing the determinant of a matrix?</li>
  <li>Where can I find information about this fastest algorithm? </li>
  </ol>
  
  <p>Thanks so much.</p>