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##

Generalization of Hermitian Case

Similar to the Lanczos methods and the Arnoldi method, the
Jacobi-Davidson method constructs a subspace onto which the given
eigenproblem is projected. The subspace is constructed with approximate
shift-and-invert steps, instead of forming a Krylov subspace. In
§4.7 we have explained the method in detail, and the
generalization to the non-Hermitian case for the basic algorithm,
described in Algorithm 4.13 (p. ),
is quite straightforward. In fact, the changes are:

- The construction of the matrix has to take into account that
is non-Hermitian, hence the corresponding action in (7)-(9) has to be
replaced by

`
`**for**

,

- In (10) a routine has to be selected for the non-Hermitian dense matrix

If the correction equation (in step (15) of the algorithm) is
solved exactly, then the approximate eigenvalues have quadratic
convergence towards the eigenvalues of .

Susan Blackford
2000-11-20