cholesky.html

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<HTML><HEAD><TITLE>Newmat09 - Cholesky decomposition</TITLE></HEAD><BODY><H2>Cholesky decomposition</H2><A HREF="qr.html">  next</A> - <A HREF="qr.html">  skip</A> - <A HREF="refer.html">  up</A> - <A HREF="index.html">  start</A><P>Suppose <TT>S</TT> is symmetric and positive definite. Then there exists aunique lower triangular matrix <TT>L</TT> such that <TT>L * L.t() = S</TT>.To calculate this use<PRE>    SymmetricMatrix S;    ......    LowerTriangularMatrix L = Cholesky(S);</PRE>If <TT>S</TT> is a symmetric band matrix then <TT>L</TT> is a band matrix and analternative procedure is provided for carrying out the decomposition:<PRE>    SymmetricBandMatrix S;    ......    LowerBandMatrix L = Cholesky(S);</PRE></BODY></HTML>

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