On a deflation method for the symmetric generalized eigenvalue problem (Q1095583)

Let a matrix pencil A-\(\lambda\) B be given. Then quadratic matrices P and Q exist such that P(A-\(\lambda\) B)Q has the Kronecker canonical form. In the paper, symmetric pencils are considered. A generalization of a reduction which was proposed by \textit{G. Fix} and \textit{R. Heiberger} [SIAM J. Numer. Anal. 9, 78-88 (1972; Zbl 0252.65028)] is used to deflate the infinite and the singular part from the pencil. It is then possible to determine the finite eigenvalues from the remaining problem. Finally, the structure of the canonical form is discussed if B is positive semidefinite.