Ritz and Pseudo-Ritz values using matrix polynomials
نویسندگان
چکیده
منابع مشابه
Majorization : Angles , Ritz Values
Many inequality relations between real vector quantities can be succinctly expressed as “weak (sub)majorization” relations using the symbol ≺w. We explain these ideas and apply them in several areas: angles between subspaces, Ritz values, and graph Laplacian spectra, which we show are all surprisingly related. Let Θ(X ,Y) be the vector of principal angles in nondecreasing order between subspace...
متن کاملThe convergence of harmonic Ritz values, harmonic Ritz vectors and refined harmonic Ritz vectors
This paper concerns a harmonic projection method for computing an approximation to an eigenpair (λ, x) of a large matrix A. Given a target point τ and a subspace W that contains an approximation to x, the harmonic projection method returns an approximation (μ + τ, x̃) to (λ, x). Three convergence results are established as the deviation of x from W approaches zero. First, the harmonic Ritz value...
متن کاملHarmonic Ritz Values and Their Reciprocals
One application of harmonic Ritz values is to approximate, with a projection method, the interior eigenvalues of a matrix A while avoiding the explicit use of the inverse A. In this context, harmonic Ritz values are commonly derived from a Petrov-Galerkin condition for the residual of a vector from the test space. In this paper, we investigate harmonic Ritz values from a slightly different pers...
متن کاملRitz and harmonic Ritz values and the convergence of FOM and GMRES
FOM and GMRES are Krylov subspace iterative methods for solving nonsymmetric linear systems. The Ritz values are approximate eigenvalues, which can be computed cheaply within these algorithms. In this paper, we generalise the concept of Harmonic Ritz values, introduced by Paige et al. for symmetric matrices, to nonsymmetric matrices. We show that the zeroes of the residual polynomials of FOM an...
متن کاملOn the Convergence of Rational Ritz Values
Ruhe’s rational Krylov method is a popular tool for approximating eigenvalues of a given matrix, though its convergence behavior is far from being fully understood. Under fairly general assumptions we characterize in an asymptotic sense which eigenvalues of a Hermitian matrix are approximated by rational Ritz values and how fast this approximation takes place. Our main tool is a constrained ext...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1996
ISSN: 0024-3795
DOI: 10.1016/0024-3795(95)00682-6