slepc-main 2024-11-22

DSHEP

Dense Hermitian Eigenvalue Problem.

Notes

The problem is expressed as A*X = X*Lambda, where A is real symmetric (or complex Hermitian). Lambda is a diagonal matrix whose diagonal elements are the arguments of DSSolve(). After solve, A is overwritten with Lambda.

In the intermediate state A is reduced to tridiagonal form. In compact storage format, the symmetric tridiagonal matrix is stored in T.

Used DS matrices

	DS_MAT_A	- problem matrix (used only if compact=false)
	DS_MAT_T	- symmetric tridiagonal matrix
	DS_MAT_Q	- orthogonal/unitary transformation that reduces to tridiagonal form (intermediate step) or matrix of orthogonal eigenvectors, which is equal to X

Implemented methods

	0	- Implicit QR (_steqr)
	1	- Multiple Relatively Robust Representations (_stevr)
	2	- Divide and Conquer (_stedc)
	3	- Block Divide and Conquer (real scalars only)

Level

beginner

Location