slepc-3.21.1 2024-04-26
Report Typos and Errors


Computes the Cholesky factor of the solution of a dense Lyapunov equation with an upper Hessenberg coefficient matrix.


#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  - linear matrix equation solver context
m  - number of rows and columns of H
H  - coefficient matrix
ldh  - leading dimension of H
k  - number of columns of B
B  - right-hand side matrix
ldb  - leading dimension of B
ldu  - 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)


The Lyapunov equation has the form H*X + X*H' = -B*B', where H is an mxm upper Hessenberg matrix, B is an mxk 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

LMEDenseLyapunov(), LMESolve()





Index of all LME routines
Table of Contents for all manual pages
Index of all manual pages