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authorGravatar Benoit Jacob <jacob.benoit.1@gmail.com>2010-10-15 09:44:43 -0400
committerGravatar Benoit Jacob <jacob.benoit.1@gmail.com>2010-10-15 09:44:43 -0400
commit26129229ec12961687b0414c40e10e2880beec79 (patch)
treead65b5a51cd493c96563462bd668744e55fa7f04 /doc/TopicLinearAlgebraDecompositions.dox
parentfcee1903be17a07fa07019d21162a8d5797dc6a9 (diff)
doc updates/improvements
Diffstat (limited to 'doc/TopicLinearAlgebraDecompositions.dox')
-rw-r--r--doc/TopicLinearAlgebraDecompositions.dox21
1 files changed, 5 insertions, 16 deletions
diff --git a/doc/TopicLinearAlgebraDecompositions.dox b/doc/TopicLinearAlgebraDecompositions.dox
index ad8d0abea..203a05dd8 100644
--- a/doc/TopicLinearAlgebraDecompositions.dox
+++ b/doc/TopicLinearAlgebraDecompositions.dox
@@ -112,27 +112,15 @@ namespace Eigen {
<tr><td colspan="9">\n Singular values and eigenvalues decompositions</td></tr>
<tr>
- <td>SVD</td>
- <td>-</td>
- <td>Average</td>
- <td>Good</td>
- <td>Yes</td>
- <td>Singular values/vectors, least squares</td>
- <td>Yes</td>
- <td>Average</td>
- <td>-</td>
- </tr>
-
- <tr>
- <td>JacobiSVD</td>
+ <td>JacobiSVD (two-sided)</td>
<td>-</td>
<td>Slow (but fast for small matrices)</td>
- <td>Proven</td>
+ <td>Excellent-Proven<sup><a href="#note3">3</a></sup></td>
<td>Yes</td>
<td>Singular values/vectors, least squares</td>
- <td>-</td>
+ <td>Yes (and does least squares)</td>
<td>Excellent</td>
- <td>-</td>
+ <td>R-SVD</td>
</tr>
<tr>
@@ -251,6 +239,7 @@ namespace Eigen {
<ul>
<li><a name="note1">\b 1: </a>There exist two variants of the LDLT algorithm. Eigen's one produces a pure diagonal D matrix, and therefore it cannot handle indefinite matrices, unlike Lapack's one which produces a block diagonal D matrix.</li>
<li><a name="note2">\b 2: </a>Eigenvalues, SVD and Schur decompositions rely on iterative algorithms. Their convergence speed depends on how well the eigenvalues are separated.</li>
+<li><a name="note3">\b 3: </a>Our JacobiSVD is two-sided, making for proven and optimal precision for square matrices. For non-square matrices, we have to use a QR preconditioner first. The default choice, ColPivHouseholderQR, is already very reliable, but if you want it to be proven, use FullPivHouseholderQR instead.
</ul>
\section TopicLinAlgTerminology Terminology