Skip to main content
`Ctrl`+`K`

# 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