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Software Repository
Chapter 5: Generalized Hermitian Eigenvalue Problems
A generalized Hermitian eigenvalue problem (GHEP) is given by,
Ax= lambda B x,
where A and B are Hermitian, A* = A and B^* = B.
We call the pair {A,B} of matrices
matrix pencil.
In this chapter we make the additional assumption which
A or B or alpha*A + beta*B for some scalars alpha and beta,
is positive definite, in that case we talk about a
Hermitian definite pencil.
This assumption is true for a wide class of practically
important cases, and the theory is very closely related to the
standard Hermitian eigenproblem, as expounded in Chapter 4.
If no positive definite combination exists, we could as well regard
{A,B} as a general pencil and use the theory and algorithms described
in Chapter 8.
Software
Section |
Package Name |
Language |
Comments |
5.3 |
LAPACK |
Fortran 77, C++ wrappers |
direct methods |
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5.5 |
LANZ |
Fortran 77 |
Lanczos method |
5.5 |
LANSO |
Fortran 77 |
Lanczos method |
5.5 |
PLANSO |
Fortran 77 |
parallel version of LANSO |
5.5 |
ARPACK |
Fortran 77, C++ wrapper |
implicitly restarted Lanczos method |
5.6 |
JDQZ |
Fortran 77 |
Jacobi-Davidson |
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