On eigenvalue variations of rayleigh quotient matrix pencils of a definite pencil
نویسندگان
چکیده
منابع مشابه
On Eigenvalues of a Rayleigh Quotient Matrix
This note deals with the following problem: Let A be an n X n Hermitian matrix, and Q and 0 be two n X rn (n > m > 1) matrices both with orthonormal column vectors. How do the eigenvalues of the m X m Hermitian matrix Q”AQ differ from those of the m X m Hermitian matrix QHAQ? We give a positive answer to one of the unsolved problems raised recently by Sun. In what follows, we will consider the ...
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Four classes of eigenvalue problems that admit similar min-max principles and the Cauchy interlacing inequalities as the symmetric eigenvalue problem famously does are investigated. These min-max principles pave ways for efficient numerical solutions for extreme eigenpairs by optimizing the so-called Rayleigh quotient functions. In fact, scientists and engineers have already been doing that for...
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Efficient and accurate computation of eigenvalues and eigenvectors is of fundamental importance in the accelerator physics community. Moreover, the eigensystem analysis is generally used for the identifications of many physical phenomena connected to vibrations. Therefore, various types of algorithms such that Arnoldi, Lanczos, KrylovSchur, Jacobi-Davidson etc. were implemented to solve the eig...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1994
ISSN: 0024-3795
DOI: 10.1016/0024-3795(94)90457-x