From c1c6b0f44cbfac5aeefa04b03e10950386aadb89 Mon Sep 17 00:00:00 2001 From: Martin Kronbichler Date: Tue, 5 May 2009 08:38:35 +0000 Subject: [PATCH] Update in comments of matrix norms. git-svn-id: https://svn.dealii.org/trunk@18812 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/lac/include/lac/sparse_matrix.h | 36 +++++++++++++------------ 1 file changed, 19 insertions(+), 17 deletions(-) diff --git a/deal.II/lac/include/lac/sparse_matrix.h b/deal.II/lac/include/lac/sparse_matrix.h index 247a44ebc4..9db67c178a 100644 --- a/deal.II/lac/include/lac/sparse_matrix.h +++ b/deal.II/lac/include/lac/sparse_matrix.h @@ -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; -- 2.39.5