EIGENVALUES OF $Ax~=~lambda$$Bx$ FOR REAL SYMMETRIC MATRICES $A$ AND $B$ COMPUTED BY THE HR PROCESS

Brebner, M.A.Grad, J2008-02-262008-02-261976-11-25http://hdl.handle.net/1880/45427This 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.EngComputer ScienceEIGENVALUES OF $Ax~=~lambda$$Bx$ FOR REAL SYMMETRIC MATRICES $A$ AND $B$ COMPUTED BY THE HR PROCESSunknown1976-11-1110.11575/PRISM/30469