LMEDenseHessLyapunovChol#
Computes the Cholesky factor of the solution of a dense Lyapunov equation with an upper Hessenberg coefficient matrix.
Synopsis#
#include "slepclme.h"
PetscErrorCode LMEDenseHessLyapunovChol(LME lme,PetscInt m,PetscScalar H[],PetscInt ldh,PetscInt k,PetscScalar B[],PetscInt ldb,PetscScalar U[],PetscInt ldu,PetscReal *res)
Logically Collective
Input Parameters#
lme - the linear matrix equation solver context
m - number of rows and columns of
HH - coefficient matrix
ldh - leading dimension of
Hk - number of columns of
BB - right-hand side matrix
ldb - leading dimension of
Bldu - leading dimension of
U
Output Parameters#
U - Cholesky factor of the solution
res - (optional) residual norm, on input it should contain \(h_{m+1,m}\)
Note#
The Lyapunov equation has the form \(HX + XH^* = -BB^*\), where \(H\) is an \(m\times m\) upper Hessenberg matrix, \(B\) is an \(m\times k\) matrix and the solution is expressed as \(X = U^*U\), where \(U\) is upper triangular. \(H\) is supposed to be stable.
When k=1 and the res argument is provided, the last row of X is used to
compute the residual norm of a Lyapunov equation projected via Arnoldi.
See Also#
Level#
developer
Location#
Index of all LME routines Table of Contents for all manual pages Index of all manual pages