]> https://gitweb.dealii.org/ - dealii.git/commitdiff
Update in comments of matrix norms.
authorMartin Kronbichler <kronbichler@lnm.mw.tum.de>
Tue, 5 May 2009 08:38:35 +0000 (08:38 +0000)
committerMartin Kronbichler <kronbichler@lnm.mw.tum.de>
Tue, 5 May 2009 08:38:35 +0000 (08:38 +0000)
git-svn-id: https://svn.dealii.org/trunk@18812 0785d39b-7218-0410-832d-ea1e28bc413d

deal.II/lac/include/lac/sparse_matrix.h

index 247a44ebc43d8bf28895ed6bd004b2026a6c42f0..9db67c178ab93645608bd23635ac6026b9a52104 100644 (file)
@@ -1486,29 +1486,31 @@ class SparseMatrix : public virtual Subscriptor
 //@{
     
                                     /**
-                                     * Return the l1-norm of the matrix, that is
-                                     * $|M|_1=max_{all columns j}\sum_{all 
-                                     * rows i} |M_ij|$,
-                                     * (max. sum of columns).
-                                     * This is the
-                                     * natural matrix norm that is compatible
-                                     * to the l1-norm for vectors, i.e.
+                                     * Return the $l_1$-norm of the matrix,
+                                     * that is $|M|_1=\max_{\mathrm{all\
+                                     * columns\ }j}\sum_{\mathrm{all\ rows\
+                                     * } i} |M_{ij}|$, (max. sum of
+                                     * columns).  This is the natural
+                                     * matrix norm that is compatible to
+                                     * the $l_1$-norm for vectors, i.e.
                                      * $|Mv|_1\leq |M|_1 |v|_1$.
-                                     * (cf. Haemmerlin-Hoffmann : Numerische Mathematik)
+                                     * (cf. Haemmerlin-Hoffmann :
+                                     * Numerische Mathematik)
                                      */
     real_type l1_norm () const;
 
                                     /**
-                                     * Return the linfty-norm of the
+                                     * Return the $l_\infty$-norm of the
                                      * matrix, that is
-                                     * $|M|_infty=max_{all rows i}\sum_{all 
-                                     * columns j} |M_ij|$,
-                                     * (max. sum of rows).
-                                     * This is the
-                                     * natural matrix norm that is compatible
-                                     * to the linfty-norm of vectors, i.e.
-                                     * $|Mv|_infty \leq |M|_infty |v|_infty$.
-                                     * (cf. Haemmerlin-Hoffmann : Numerische Mathematik)
+                                     * $|M|_\infty=\max_{\mathrm{all\ rows\
+                                     * }i}\sum_{\mathrm{all\ columns\ }j}
+                                     * |M_{ij}|$, (max. sum of rows).  This
+                                     * is the natural matrix norm that is
+                                     * compatible to the $l_\infty$-norm of
+                                     * vectors, i.e.  $|Mv|_\infty \leq
+                                     * |M|_\infty |v|_\infty$.
+                                     * (cf. Haemmerlin-Hoffmann :
+                                     * Numerische Mathematik)
                                      */
     real_type linfty_norm () const;
 

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