bug #1538: update manual pages regarding BDCSVD.

doc/LeastSquares.dox

@@ -16,7 +16,7 @@ equations is the fastest but least accurate, and the QR decomposition is in betw
 
 \section LeastSquaresSVD Using the SVD decomposition
 
-The \link JacobiSVD::solve() solve() \endlink method in the JacobiSVD class can be directly used to
+The \link BDCSVD::solve() solve() \endlink method in the BDCSVD class can be directly used to
 solve linear squares systems. It is not enough to compute only the singular values (the default for
 this class); you also need the singular vectors but the thin SVD decomposition suffices for
 computing least squares solutions:

doc/TopicLinearAlgebraDecompositions.dox

@@ -4,7 +4,7 @@ namespace Eigen {
 
 This page presents a catalogue of the dense matrix decompositions offered by Eigen.
 For an introduction on linear solvers and decompositions, check this \link TutorialLinearAlgebra page \endlink.
-To get an overview of the true relative speed of the different decomposition, check this \link DenseDecompositionBenchmark benchmark \endlink.
+To get an overview of the true relative speed of the different decompositions, check this \link DenseDecompositionBenchmark benchmark \endlink.
 
 \section TopicLinAlgBigTable Catalogue of decompositions offered by Eigen
 
@@ -113,6 +113,18 @@ To get an overview of the true relative speed of the different decomposition, ch
 
     <tr><th class="inter" colspan="9">\n Singular values and eigenvalues decompositions</th></tr>
 
+    <tr>
+        <td>BDCSVD (divide \& conquer)</td>
+        <td>-</td>
+        <td>One of the fastest SVD algorithms</td>
+        <td>Excellent</td>
+        <td>Yes</td>
+        <td>Singular values/vectors, least squares</td>
+        <td>Yes (and does least squares)</td>
+        <td>Excellent</td>
+        <td>Blocked bidiagonalization</td>
+    </tr>
+
     <tr>
         <td>JacobiSVD (two-sided)</td>
         <td>-</td>

doc/TutorialLinearAlgebra.dox

@@ -73,7 +73,7 @@ depending on your matrix and the trade-off you want to make:
         <td>ColPivHouseholderQR</td>
         <td>colPivHouseholderQr()</td>
         <td>None</td>
-        <td>++</td>
+        <td>+</td>
         <td>-</td>
         <td>+++</td>
     </tr>
@@ -85,6 +85,14 @@ depending on your matrix and the trade-off you want to make:
         <td>- -</td>
         <td>+++</td>
     </tr>
+    <tr class="alt">
+        <td>CompleteOrthogonalDecomposition</td>
+        <td>completeOrthogonalDecomposition()</td>
+        <td>None</td>
+        <td>+</td>
+        <td>-</td>
+        <td>+++</td>
+    </tr>
     <tr class="alt">
         <td>LLT</td>
         <td>llt()</td>
@@ -101,15 +109,24 @@ depending on your matrix and the trade-off you want to make:
         <td>+</td>
         <td>++</td>
     </tr>
+    <tr class="alt">
+        <td>BDCSVD</td>
+        <td>bdcSvd()</td>
+        <td>None</td>
+        <td>-</td>
+        <td>-</td>
+        <td>+++</td>
+    </tr>
     <tr class="alt">
         <td>JacobiSVD</td>
         <td>jacobiSvd()</td>
         <td>None</td>
-        <td>- -</td>
+        <td>-</td>
         <td>- - -</td>
         <td>+++</td>
     </tr>
 </table>
+To get an overview of the true relative speed of the different decompositions, check this \link DenseDecompositionBenchmark benchmark \endlink.
 
 All of these decompositions offer a solve() method that works as in the above example.
 
@@ -183,8 +200,11 @@ Here is an example:
 
 \section TutorialLinAlgLeastsquares Least squares solving
 
-The most accurate method to do least squares solving is with a SVD decomposition. Eigen provides one
-as the JacobiSVD class, and its solve() is doing least-squares solving.
+The most accurate method to do least squares solving is with a SVD decomposition.
+Eigen provides two implementations.
+The recommended one is the BDCSVD class, which scale well for large problems
+and automatically fall-back to the JacobiSVD class for smaller problems.
+For both classes, their solve() method is doing least-squares solving.
 
 Here is an example:
 <table class="example">

doc/examples/TutorialLinAlgSVDSolve.cpp

@@ -11,5 +11,5 @@ int main()
    VectorXf b = VectorXf::Random(3);
    cout << "Here is the right hand side b:\n" << b << endl;
    cout << "The least-squares solution is:\n"
-        << A.jacobiSvd(ComputeThinU | ComputeThinV).solve(b) << endl;
+        << A.bdcSvd(ComputeThinU | ComputeThinV).solve(b) << endl;
 }