DSNHEP#

Dense Non-Hermitian Eigenvalue Problem.

Notes#

The problem is expressed as \(AX = X\Lambda\), where \(A\) is the input matrix. \(\Lambda\) is a diagonal matrix whose diagonal elements are the arguments of DSSolve(). After solve, \(A\) is overwritten with the upper quasi-triangular matrix \(T\) of the (real) Schur form, \(AQ = QT\).

In the intermediate state \(A\) is reduced to upper Hessenberg form.

Computation of left eigenvectors is supported, but two-sided Krylov solvers usually rely on the related DSNHEPTS.

Used DS matrices#

  • DS_MAT_A - problem matrix

  • DS_MAT_Q - orthogonal/unitary transformation that reduces to Hessenberg form (intermediate step) or matrix of orthogonal Schur vectors

Implemented methods#

  • 0 - Implicit QR (_hseqr)

See Also#

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

Level#

beginner

Location#

src/sys/classes/ds/impls/nhep/dsnhep.c

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