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 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 \(HX + XH^* = -BB^*\), 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#

LME: Linear Matrix Equation, LMEDenseLyapunov(), LMESolve()

Level#

developer

Location#

src/lme/interface/lmedense.c

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