slepc-3.21.1 2024-04-26
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# DSNHEP

Dense Non-Hermitian Eigenvalue Problem.

### Notes

The problem is expressed as A*X = 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, A*Q = Q*T.

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

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