diff options
Diffstat (limited to 'src/Rips_complex/doc/Intro_rips_complex.h')
| -rw-r--r-- | src/Rips_complex/doc/Intro_rips_complex.h | 6 |
1 files changed, 4 insertions, 2 deletions
diff --git a/src/Rips_complex/doc/Intro_rips_complex.h b/src/Rips_complex/doc/Intro_rips_complex.h index f9663315..909735cd 100644 --- a/src/Rips_complex/doc/Intro_rips_complex.h +++ b/src/Rips_complex/doc/Intro_rips_complex.h @@ -82,12 +82,14 @@ namespace rips_complex { * filtered simplicial complex (linear size, with constants that depend on * ε and the doubling dimension of the space) that is * \f$(1+O(\epsilon))-\f$interleaved with it (in particular, their persistence - * diagrams are at log-bottleneck distance at most ε). + * diagrams are at log-bottleneck distance at most \f$O(\epsilon)\f$). * * The sparse Rips filtration was introduced by Don Sheehy * \cite sheehy13linear. We are using the version from \cite buchet16efficient * (except that we multiply all filtration values by 2, to match the usual - * Rips complex). + * Rips complex), which proves a + * \f$\frac{1+\epsilon}{1-\epsilon}\f$-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. * |