Matrix functions

We consider the solution of the linear matrix function equation

(11)\[\begin{align}\label{eq:matrixfunc} \vec{x} = f(A) \vec{b} \end{align}\]

for the vector \(\vec{x}\) and \(\vec{b}\) with a given square matrix \(A\in \mathbb{R}^{n \times n}\). The matrix \(A\) is assumed to be self-adjoint in the scalar product defined by the symmetric and positiv definit matrix \(M\)

(12)\[\begin{align} \langle \vec v, \vec w\rangle_M := \vec v^\mathrm{T} M \cdot \vec w ,\quad ||\vec v||_M := \sqrt{ \langle \vec v, \vec v\rangle_M} \end{align}\]

Include and Link

When you use the matrix-function extension you will need to have boost and lapack installed on your system. On linux, installing libboost-dev and liblapacke-dev should suffice. When configuring on a non-default system add lapack to the LIBLAPACK configuration variable in the Makefile.

#include "dg/algorithm.h"
#include "dg/matrix/matrix.h" //requires boost and lapacke

to be continued … (check out doxygen documentation for now)