A class of quasipure injective Abelian groups

A Davidson-Lanczos iteration method for computation of continued-fraction expansion of the Green's function at very low temperatures: Applications to the dynamical mean field theory

“…The basic idea of Lanczos method is the construction of basis where the projection of the Hamiltonian has a tridiagonal representation. The optimization [18] of Rayleigh quotient r(x) = x T Hx/x T x, where H ∈ R n×n and x = 0 ∈ R n , leads to the problem of computing orthonormal basis q 1 , ...q n for the Krylov subspace [13]…”

“…Lanczos method is an implementation of the Rayleigh Ritz procedure [12] on a Krylov subspace [13] whereas Davidson method is on non-Krylov subspace. In this paper, we use the orignal version of Davidson method and the simplest version of the Lanczos algorithm and find that the inclusion of Davidson method in evaluation of Green's function in low temperature regime can be favourably used to our advantage.…”

Vibration of Non-Uniform Bernoulli-Euler Beam Under Moving Distributed Masses Resting on Pasternak Elastic Foundation Subjected to Variable Magnitude

“…The study of force-induced vibrations in elastic bodies, such as stretched strings, spring-mass systems, and rods, has been subject to extensive research by numerous authors (Krylov, 1905;Timoshenko, 1921;Kenney, 1954;Stanisic et al, 1968;Stanisic & Hardin, 1969;Stanisic et al, 1974;Sadiku & Leipholz, 1987;Esmailzadeh & Ghorashi, 1995;Oni, 1997;Oni & Ogunyebi, 2008;Oni & Omolofe, 2010). These vibrations may arise from (i) a force or load that is solely dependent on the spatial coordinates.…”