#include "slepclme.h" PetscErrorCode LMESetProblemType(LME lme,LMEProblemType type)Logically Collective
| lme | - the linear matrix equation solver context | |
| type | - a known type of matrix equation |
| -lme_lyapunov | - continuous-time Lyapunov equation A*X+X*A'=-C | |
| -lme_sylvester | - continuous-time Sylvester equation A*X+X*B=C | |
| -lme_gen_lyapunov | - generalized Lyapunov equation A*X*D'+D*X*A'=-C | |
| -lme_gen_sylvester | - generalized Sylvester equation A*X*E+D*X*B=C | |
| -lme_dt_lyapunov | - discrete-time Lyapunov equation A*X*A'-X=-C | |
| -lme_stein | - Stein equation A*X*E+X=C |
equation A B D E
----------------- --- --- --- ---
LME_LYAPUNOV A*X+X*A'=-C yes (A-t) - -
LME_SYLVESTER A*X+X*B=C yes yes - -
LME_GEN_LYAPUNOV A*X*D'+D*X*A'=-C yes (A-t) yes (D-t)
LME_GEN_SYLVESTER A*X*E+D*X*B=C yes yes yes yes
LME_DT_LYAPUNOV A*X*A'-X=-C yes - - (A-t)
LME_STEIN A*X*E+X=C yes - - yes
In the above table, the notation (A-t) 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.