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    <ol> <li>(optional) Understand <a href="http://en.wikipedia.org/wiki/Gaussian_elimination" rel="nofollow noreferrer">this</a>. Do some examples on paper.</li> <li><em>Don't write code for Gaussian elimination yourself</em>. Without some care, the naive gauss pivoting is unstable. You have to scale the lines and take care of pivoting with the greatest element, a starting point is <a href="http://en.wikipedia.org/wiki/Pivot_element" rel="nofollow noreferrer">there</a>. Note that this advice holds for most linear algebra algorithms.</li> <li>If you want to solve systems of equations, <a href="http://en.wikipedia.org/wiki/LU_decomposition" rel="nofollow noreferrer">LU decomposition</a>, <a href="http://en.wikipedia.org/wiki/QR_decomposition" rel="nofollow noreferrer">QR decomposition</a> (stabler than LU, but slower), <a href="http://en.wikipedia.org/wiki/Cholesky_decomposition" rel="nofollow noreferrer">Cholesky decomposition</a> (in the case the system is symmetric) or <a href="http://en.wikipedia.org/wiki/Singular_value_decomposition" rel="nofollow noreferrer">SVD</a> (in the case the system is not square) are almost always better choices. Gaussian elimination is best for computing determinants however.</li> <li>Use the algorithms from <a href="http://www.netlib.org/lapack/" rel="nofollow noreferrer">LAPACK</a> for the problems which need Gaussian elimination (eg. solving systems, or computing determinants). Really. Don't roll your own. Since you are doing C++, you may be interested in <a href="http://arma.sourceforge.net/" rel="nofollow noreferrer">Armadillo</a> which takes care of a lot of things for you.</li> <li>If you must roll your own for pedagogical reasons, have a look first at <em>Numerical Recipes, version 3</em>. Version 2 can be found online for free if you're low on budget / have no access to a library.</li> <li>As a general advice, don't code algorithms you don't understand.</li> </ol>
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    1. USAlexandre C.
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    1. COTo point 6.: for me in university it helped a lot to try to code an algorithm in order to understand it.
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    2. COYes, for production code, 6 is applicable. But for learning, it may help. Nb. 6 needs a disclaimer. Otherwise, +1.
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      1. USSebastian Mach
 

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