We generalize -pseudospectra and the associated computational algorithms to the generalized eigenvalue problem. Rank one perturbations are used to determine the -pseudospectra.

This paper presents a sequential semidefinite programming (SDP) approach to maximize the minimal eigenvalue of the generalized eigenvalue problem, in which the two symmetric matrices defining the eigenvalue problem are supposed to be the polynomials in terms of the variables. An important application of this problem is found in the structural optimization which attempts to maximize the minimal ...

It is well known that dimensionality reduction based on multivariate analysis methods and their kernelized extensions can be formulated as generalized eigenvalue problems of scatter matrices, Gram matrices or their augmented matrices. This paper provides a generic and theoretical framework of multivariate analysis introducing a new expression for scatter matrices and Gram matrices, called Gener...

It is well known that the problem of calculating the largest or smallest generalized eigenvalue problem is one of the most important problems in science and engineering 1, 2 . This problem arises naturally in many applications. Mathematically, it is a generalization of the symmetric eigenvalue problem, and it can be reduced to an equivalent symmetric eigenvalue problem. Let A,B ∈ n×n be real sy...

In a recent paper by Hirzallah et al. [O. Hirzallah, F. Kittaneh, M. Krnić, N. Lovričević, and J. Pečarić. Eigenvalue inequalities for differences of means of Hilbert space operators. Linear Algebra and its Applications, 436:1516–1527, 2012.], several eigenvalue inequalities are obtained for the difference of weighted arithmetic and weighted geometric means of two positive invertible operators ...