LMESetProblemType#

Specifies the type of matrix equation to be solved.

Synopsis#

#include "slepclme.h" 
PetscErrorCode LMESetProblemType(LME lme,LMEProblemType type)

Logically Collective

Input Parameters#

lme - the linear matrix equation solver context
type - a known type of matrix equation

Options Database Keys#

-lme_lyapunov - continuous-time Lyapunov equation
-lme_sylvester - Sylvester equation
-lme_gen_lyapunov - generalized Lyapunov equation
-lme_gen_sylvester - generalized Sylvester equation
-lme_dt_lyapunov - discrete-time Lyapunov equation
-lme_stein - Stein equation

Notes#

The coefficient matrices \(A\), \(B\), \(D\), \(E\) must be provided via LMESetCoefficients(), but some of them are optional depending on the matrix equation.

Problem Type	Equation	`LMEProblemType`	\(A\)	\(B\)	\(D\)	\(E\)
Continuous-Time Lyapunov	\(AX+XA^*=-C\)	`LME_LYAPUNOV`	yes	\(A^*\)	-	-
Sylvester	\(AX+XB=C\)	`LME_SYLVESTER`	yes	yes	-	-
Generalized Lyapunov	\(AXD^+DXA^=-C\)	`LME_GEN_LYAPUNOV`	yes	\(A^*\)	yes	\(D^*\)
Generalized Sylvester	\(AXE+DXB=C\)	`LME_GEN_SYLVESTER`	yes	yes	yes	yes
Discrete-Time Lyapunov	\(AXA^*-X=-C\)	`LME_DT_LYAPUNOV`	yes	-	-	\(A^*\)
Stein	\(AXE-X=-C\)	`LME_STEIN`	yes	-	-	yes

In the above table, the notation \(A^*\) means that this matrix need not be passed, but the user may choose to pass an explicit transpose of matrix \(A\) (for improved efficiency).

Also note that some of the equation types impose restrictions on the properties of the coefficient matrices and possibly on the right-hand side \(C\).