slepc-3.12.2 2020-01-13
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# LMEDenseLyapunovFact

Computes the Cholesky factor of the solution of a dense Lyapunov equation with rank-1 right-hand side.

### Synopsis

    #include "slepclme.h"
    PetscErrorCode LMEDenseLyapunovChol(LME lme,PetscScalar *H,PetscInt m,PetscInt ldh,PetscScalar *r,PetscScalar *L,PetscInt ldl,PetscReal *res)

Logically Collective on lme

### Input Parameters

| lme | - linear matrix equation solver context
| H | - coefficient matrix
| m | - problem size
| ldh | - leading dimension of H
| r | - right-hand side vector
| ldl | - leading dimension of L

### Output Parameter

| L | - Cholesky factor of the solution
| res | - residual norm

### Note

The Lyapunov equation has the form H*X + X*H' = -r*r', where H represents the leading mxm submatrix of argument H, and the solution X = L*L'.

H is assumed to be in upper Hessenberg form, with dimensions (m+1)xm. The last row is used to compute the residual norm, assuming H and r come from the projection onto an Arnoldi basis.

### See Also

LMESolve()

Location: src/lme/interface/lmedense.c
Index of all LME routines
Table of Contents for all manual pages
Index of all manual pages