diff --git a/README.md b/README.md index 2636c75..9e8e3dd 100644 --- a/README.md +++ b/README.md @@ -9,10 +9,15 @@ $$ K = \text{\textbf{tril}}(UV^\top) + \text{\textbf{triu}}\left(VU^\top,1\right), \quad U,V\in\mathbb{R}^{n\times p} $$ +$$ +K = \text{\textbf{tril}}(UV^\top) + \text{\textbf{triu}}\left(VU^\top,1\right) + \lambda I, \quad U,V\in\mathbb{R}^{n\times p},\ \lambda\in\mathbb{R} +$$ + $$ K = \text{\textbf{tril}}(UV^\top) + \text{\textbf{triu}}\left(VU^\top,1\right) + \text{\textbf{diag}}(d), \quad U,V\in\mathbb{R}^{n\times p},\ d\in\mathbb{R}^n $$ + All implemented algorithms (multiplication, Cholesky factorization, forward/backward substitution as well as various traces and determinants) scales with $O(p^kn)$. Since $p \ll n$ this result in very scalable computations. A more in-depth descriptions of the algorithms can be found in [1] or [here](https://github.com/mipals/SmoothingSplines.jl/blob/master/mt_mikkel_paltorp.pdf).