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Generalized Symmetric Definite Eigenproblems (GSEP)

Drivers are provided to compute all the eigenvalues and (optionally) the eigenvectors of the following types of problems:

  1. $A z = \lambda B z$
  2. $A B z = \lambda z$
  3. $B A z = \lambda z$
where $A$ and $B$ are symmetric or Hermitian and $B$ is positive definite. For all these problems the eigenvalues $\lambda$ are real. The matrices $Z$ of computed eigenvectors satisfy $Z^T A Z = \Lambda$ (problem types 1 and 3) or $Z^{-1} A Z^{-T} = I$ (problem type 2), where $\Lambda$ is a diagonal matrix with the eigenvalues on the diagonal. $Z$ also satisfies $Z^T B Z = I$ (problem types 1 and 2) or $Z^T B^{-1} Z = I$ (problem type 3).
There are three types of driver routines for generalized symmetric and Hermitian eigenproblems. Originally LAPACK had just the simple and expert drivers described below, and the third driver was added after an improved algorithm was discovered.
Different driver routines are provided to take advantage of special structure or storage of the matrices $A$ and $B$, as shown in Table 2.6.
next up previous contents index
Next: Generalized Nonsymmetric Eigenproblems (GNEP) Up: Generalized Eigenvalue and Singular Previous: Generalized Eigenvalue and Singular   Contents   Index
Susan Blackford 2001-08-19