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|Title:||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.|
|Appears in Collections:||Brebner, Mike|
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