slepc-3.22.2 2024-12-02

DSPEP

Dense Polynomial Eigenvalue Problem.

Notes

The problem is expressed as P(lambda)*x = 0, where P(.) is a matrix polynomial of degree d. The eigenvalues lambda are the arguments returned by DSSolve().

The degree of the polynomial, d, can be set with DSPEPSetDegree(), with the first d+1 extra matrices of the DS defining the matrix polynomial. By default, the polynomial is expressed in the monomial basis, but a different basis can be used by setting the corresponding coefficients via DSPEPSetCoefficients().

The problem is solved via linearization, by building a pencil (A,B) of size p*n and solving the corresponding GNHEP.

Used DS matrices

	DS_MAT_Ex	- coefficients of the matrix polynomial
	DS_MAT_X	- right eigenvectors
	DS_MAT_Y	- left eigenvectors
	DS_MAT_A	- (workspace) first matrix of the linearization
	DS_MAT_B	- (workspace) second matrix of the linearization
	DS_MAT_W	- (workspace) right eigenvectors of the linearization
	DS_MAT_U	- (workspace) left eigenvectors of the linearization

Implemented methods

- QZ iteration on the linearization (_ggev)

Level

beginner

Location