Solvers

Table of Contents

Introduction

This section describes the linear solver options available to solve the matrix system

\[ \mat{A} \vec{x} = \vec{B} \]

where

\( \mat{A} \) = coefficient matrix
\( \vec{x} \) = vector of unknowns
\( \vec{B} \) = source vector

If the coefficient matrix only has values on its diagonal, the solution vector can be obtained inverting the matrix system:

\[ \vec{x} = \mat{A}^{-1} \vec{B} \]

Where the inverse of the diagonal matrix is simply:

\[ \mat{A}^{-1} = \frac{1}{\mathrm{diag}(\mat{A})} \]

This is available as the diagonalSolver. More typically the matrix cannot be inverted easily and the system is solved using iterative methods, as described in the following sections.

Options

Solver options include:

Solver control

Common usage

Implementation details

Matrix structure

Matrix coefficients are stored in upper-triangular order

Further information