slepc-main 2024-12-17

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	- 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)

Note

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.

Level

developer

Location

src/lme/interface/lmedense.c

Index of all LME routines
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