DSGNHEP#

Dense Generalized Non-Hermitian Eigenvalue Problem.

Notes#

The problem is expressed as \(AX = BX\Lambda\), where \((A,B)\) is the input matrix pencil. \(\Lambda\) is a diagonal matrix whose diagonal elements are the arguments of DSSolve(). After solve, \((A,B)\) is overwritten with the generalized (real) Schur form \((S,T) = (Z^*AQ,Z^*BQ)\), with the first matrix being upper quasi-triangular and the second one triangular.

Used DS matrices#

  • DS_MAT_A - first problem matrix

  • DS_MAT_B - second problem matrix

  • DS_MAT_Q - first orthogonal/unitary transformation that reduces to generalized (real) Schur form

  • DS_MAT_Z - second orthogonal/unitary transformation that reduces to generalized (real) Schur form

Implemented methods#

  • 0 - QZ iteration (_gges)

  • 1 - blocked QZ iteration (_gges3, if available)

See Also#

DS: Direct Solver (or Dense System), DSCreate(), DSSetType(), DSType

Level#

beginner

Location#

src/sys/classes/ds/impls/gnhep/dsgnhep.c

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