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Generalized Symmetric Definite Eigenproblems (GSEP)

  

   An expert driver  is provided to compute all the eigenvalues and (optionally) the eigenvectors of the following types of problems:

  1. tex2html_wrap_inline12875
  2. tex2html_wrap_inline12877
  3. tex2html_wrap_inline12879

where A and B are symmetric or Hermitian and B is positive definite. For all these problems the eigenvalues  tex2html_wrap_inline12778 are real. When A and B are symmetric, the matrices Z of computed eigenvectors  satisfy tex2html_wrap_inline12895 (problem types 1 and 3) or tex2html_wrap_inline12897 (problem type 2), where tex2html_wrap_inline12784 is a diagonal matrix with the eigenvalues on the diagonal. Z also satisfies tex2html_wrap_inline12903 (problem types 1 and 2) or tex2html_wrap_inline12905 (problem type 3). When A and B are Hermitian, the matrices Z of computed eigenvectors  satisfy tex2html_wrap_inline12913 (problem types 1 and 3) or tex2html_wrap_inline12915 (problem type 2), where tex2html_wrap_inline12784 is a diagonal matrix with the eigenvalues on the diagonal. Z also satisfies tex2html_wrap_inline12921 (problem types 1 and 2) or tex2html_wrap_inline12923 (problem type 3).

The routine is listed in table 3.5.

  table1135
Table 3.5: Driver routine for the generalized symmetric definite eigenvalue problems



Susan Blackford
Tue May 13 09:21:01 EDT 1997