EIGENVALUES OF $Ax~=~lambda$$Bx$ FOR REAL SYMMETRIC MATRICES $A$ AND $B$ COMPUTED BY THE HR PROCESS
Abstract
This paper presents a method for solving the eigenvalue problem
$Ax~=~lambda$$Bx$, where $A$ and $B$ are real symmetric but not
necessarily positive definite matrices, and $B$ is nonsingular. The
method reduces the general case into a form $Cz~=~lambda$$z$ where $C$
is a pseudo-symmetric matrix. A further reduction of $C$ produces a
tridiagonal pseudo-symmetric form to which the interactive HR process
is applied. The tridiagonal pseudo-symmetric form is invariant under
the HR transformations. The amount of computation is significantly
less than treating the problem by a general method.
Description
Keywords
Computer Science