Generalized Rayleigh quotients and generating vectors
Natália Bebiano, João da Providência, Ana Nata, João P. da Providência · Linear and Multilinear Algebra · 2016
This article is concerned with the following problem: given , of which either A or B is Hermitian, and given , determine a vector such that with , referred to as a generalized Rayleigh quotient. Such a vector w is called a generating vector for z. Our approach builds on the fact that the field of values of a linear pencil can be accurately approximated under the compression into bidimensional linear pencils, in which case the problem has an exact solution. The efficiency of the presented algorithms is discussed and numerical examples are included.