slepc-3.22.2 2024-12-02
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# 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)

### See Also

DSCreate(), DSSetType(), DSType

### Level

beginner

### Location

src/sys/classes/ds/impls/hep/dshep.c
Index of all DS routines
Table of Contents for all manual pages
Index of all manual pages