slepc-3.21.1 2024-04-26
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# DSNEP

Dense Nonlinear Eigenvalue Problem.

### Notes

The problem is expressed as T(lambda)*x = 0, where T(lambda) is a parameter-dependent matrix written as T(lambda) = sum_i E_i*f_i(lambda). The eigenvalues lambda are the arguments returned by DSSolve()..

The coefficient matrices E_i are the extra matrices of the DS, and the scalar functions f_i are passed via DSNEPSetFN(). Optionally, a callback function to fill the E_i matrices can be set with DSNEPSetComputeMatrixFunction().

### Used DS matrices

| DS_MAT_Ex | - coefficient matrices of the split form of T(lambda)
| DS_MAT_A | - (workspace) T(lambda) evaluated at a given lambda (SLP only)
| DS_MAT_B | - (workspace) T'(lambda) evaluated at a given lambda (SLP only)
| DS_MAT_Q | - (workspace) left Hankel matrix (contour only)
| DS_MAT_Z | - (workspace) right Hankel matrix (contour only)
| DS_MAT_U | - (workspace) left singular vectors (contour only)
| DS_MAT_V | - (workspace) right singular vectors (contour only)
| DS_MAT_W | - (workspace) auxiliary matrix of size nxn

### Implemented methods

| 0 | - Successive Linear Problems (SLP), computes just one eigenpair
| 1 | - Contour integral, computes all eigenvalues inside a region

### See Also

DSCreate(), DSSetType(), DSType, DSNEPSetFN(), DSNEPSetComputeMatrixFunction()

### Level

beginner

### Location

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