What we plan to include

The following description is very terse. The user will see a more extended description of each problem, including common synonyms.

1. Hermitian eigenproblem

2. Non-Hermitian eigenproblem

3. Generalized definite eigenproblem , where ,

4. Generalized Hermitian eigenproblem , where ,

5. Generalized non-Hermitian eigenproblem , where

6. Generalized non-Hermitian Eigenproblem

7. Quadratic or higher degree eigenvalue problems

8. Singular Value Decomposition (SVD) of a single general matrix

9. Generalized SVD of and

10. Other eigenvalue problems

Note that this list does include all the possible variations hinted at in the previous section; these will appear as the user traverses the tree. For example, there will be cross references to other, better algorithms in cases for which simple transformations permit their use. Here are some examples:

• Under ``Hermitian eigenproblem '': If , the user will be advised to consider the SVD of .

• Under ``Generalized Hermitian eigenproblem'': If and , and the user knows real constants and such that is positive definite, the user will be advised to consider the definite eigenproblem .

• Under ``Non-Hermitian eigenproblem '': If is Hermitian for known, simple and , the user will be advised to consider the eigenproblem for .

• Under ``SVD of '': If , the user will be advised to consider the quotient SVD of and .

• Under ``Quadratic or higher degree eigenvalue problems'', the user will be advised to consider the linearization of problem to a matrix pencil eigenvalue problem.
• Under ``Other eigenvalue problems'', the user will see some other related eigenvalue problems, such as
  • Updating eigendecompositions
  • Polynomial zero finding
  • Rank revealing QR decomposition