Template for the Solution of Algebraic Eigenvalue Problems:
  A Practical Guide

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
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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