diff options
Diffstat (limited to 'src/Rips_complex/doc')
-rw-r--r-- | src/Rips_complex/doc/Intro_rips_complex.h | 7 |
1 files changed, 5 insertions, 2 deletions
diff --git a/src/Rips_complex/doc/Intro_rips_complex.h b/src/Rips_complex/doc/Intro_rips_complex.h index a2537036..1aac804b 100644 --- a/src/Rips_complex/doc/Intro_rips_complex.h +++ b/src/Rips_complex/doc/Intro_rips_complex.h @@ -92,8 +92,8 @@ namespace rips_complex { * The sparse Rips filtration was introduced by Don Sheehy * \cite sheehy13linear. We are using the version described in * \cite buchet16efficient (except that we multiply all filtration values - * by 2, to match the usual Rips complex), which proves a - * \f$\frac{1+\epsilon}{1-\epsilon}\f$-interleaving, although in practice the + * by 2, to match the usual Rips complex), for which \cite cavanna15geometric proves a + * \f$(1,\frac{1}{1-\epsilon})\f$-interleaving, although in practice the * error is usually smaller. * A more intuitive presentation of the idea is available in * \cite cavanna15geometric, and in a video \cite cavanna15visualizing. @@ -107,6 +107,9 @@ namespace rips_complex { * Theoretical guarantees are only available for \f$\epsilon<1\f$. The * construction accepts larger values of ε, and the size of the complex * keeps decreasing, but there is no guarantee on the quality of the result. + * Note that while the number of edges decreases when ε increases, the + * number of higher-dimensional simplices may not be monotonous when + * \f$\frac12\leq\epsilon\leq 1\f$. * * \section ripspointsdistance Point cloud and distance function * |