diff --git a/README.md b/README.md index 506aa40..239626d 100644 --- a/README.md +++ b/README.md @@ -6,11 +6,11 @@ A package for efficiently computing with symmetric extended generator representable semiseparable matrices (EGRSS Matrices) and a variant with added diagonal terms. In short this means matrices of the form $$ -K = \text{\textbf{tril}}(UV^\top) + \text{\textbf{triu}}\left(VU^\top,1\right), \quad U,V\in\mathbb{R}^{p\times n} +K = \text{\textbf{tril}}(UV^\top) + \text{\textbf{triu}}\left(VU^\top,1\right), \quad U,V\in\mathbb{R}^{n\times p} $$ $$ -K = \text{\textbf{tril}}(UV^\top) + \text{\textbf{triu}}\left(VU^\top,1\right) + \text{\textbf{diag}}(d), \quad U,V\in\mathbb{R}^{p\times n},\ d\in\mathbb{R}^n +K = \text{\textbf{tril}}(UV^\top) + \text{\textbf{triu}}\left(VU^\top,1\right) + \text{\textbf{diag}}(d), \quad U,V\in\mathbb{R}^{n\times p},\ d\in\mathbb{R}^n $$ 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.