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来自「矩阵算法库newmat10.tar.gz的帮助文件」· HTML 代码 · 共 46 行

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<HTML><HEAD><TITLE>Newmat09 - Singular value decomposition</TITLE></HEAD><BODY><H2>Singular value decomposition</H2><A HREF="evalues.html">  next</A> - <A HREF="evalues.html">  skip</A> - <A HREF="refer.html">  up</A> - <A HREF="index.html">  start</A><P>The singular value decomposition of an m x n <TT>Matrix</TT> <TT>A</TT>(where m >= n) is a decomposition<PRE>    A  = U * D * V.t()</PRE>where <TT>U</TT> is m x n with  <TT>U.t() * U</TT>  equalling the identity,<TT>D</TT> is an n x n<TT>DiagonalMatrix</TT> and <TT>V</TT> is an n x n orthogonal matrix(type <TT>Matrix</TT> in <I>Newmat</I>).<P>Singular value decompositions are useful for understanding the structureof ill-conditioned matrices, solving least squares problems, and forfinding the eigenvalues of <TT>A.t() * A</TT>.<P>To calculate the singular value decomposition of <TT>A</TT>(with m >= n) use one of<PRE>    SVD(A, D, U, V);                  // U = A is OK    SVD(A, D);    SVD(A, D, U);                     // U = A is OK    SVD(A, D, U, false);              // U (can = A) for workspace only    SVD(A, D, U, V, false);           // U (can = A) for workspace only</PRE>where <TT>A</TT>, <TT>U</TT> and <TT>V</TT> are of type <TT>Matrix</TT> and<TT>D</TT>is a <TT>DiagonalMatrix</TT>. The values of <TT>A</TT> are not changed unless <TT>A</TT> is alsoinserted as the third argument.<P><A HREF="evalues.html">  next</A> - <A HREF="evalues.html">  skip</A> - <A HREF="refer.html">  up</A> - <A HREF="index.html">  start</A><P></BODY></HTML>

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