It is well known that the performance of eigenvalue algorithms such as the Lanczos and the Arnoldi method depends on the distribution of eigenvalues. Under fairly general assumptions we characterize the region of good convergence for the Isometric Arnoldi Process. We also determine bounds for the rate of convergence and we prove sharpness of these bounds. The distribution of isometric Ritz valu...

A retrospective evaluation of attitudinal, behavioural and knowledge change among diverse stakeholder groups was conducted in Limpopo Province of South Africa to assess the effectiveness of a series of values clarification (VC) interventions. Telephone and face-to-face interview (193) results revealed that over two-thirds (70.2%) reported behavioural changes and 93.2% reported increased compass...

1 Why and how The Lanczos method is quite eeective if the desired eigenvalue is either max or min and if this eigenvalue is relatively well separated from the remaining spectrum, or when the method is applied with (A ? I) ?1 , for some reasonable guess for an eigenvalue. If none of these conditions is fulllled, for instance the computation of a vector (A ? I) ?1 y for given y may be computation...

The article touches upon the problem of natural oscillations a thin elastic wavy shell an open profile. proposed method for determining numerical values lowest frequencies and corresponding forms shells complicated shape is based on Rayleigh-Ritz energy method.
 results calculation this with hinge-fixed attachment along lower contour generatrix are presented.

While discussing the convergence of the Lanczos method, Trefethen and Bau observed a relationship with electric charge distributions, and claimed that the Lanczos iteration tends to converge to eigenvalues in regions of \too little charge" for an equilibrium distribution. Recently, Kuijlaars found a theoretical justiication for this phenomenon by considering the Lanczos method applied to a suit...

Abstract: Condition numbers for infinite-dimensional optimization, as defined in Zolezzi (2002, 2003), are shown to exhibit a stable behavior when employing finite-dimensional solution methods of the Ritz type, in particular finite elements. The same behavior is shown to hold in connection with the so called extended Ritz method.

We discuss a novel form of the variational approach in Quantum Field Theory in which the trial quantum configuration is represented directly in terms of relevant expectation values rather than, e.g., increasingly complicated structure from Fock space. The quantum algebra imposes constraints on such expectation values so that the variational problem is formulated here as an optimization under co...

It is well known how any symmetric matrix can be reduced by an orthogonal similarity transformation into tridiagonal form. Once the tridiagonal matrix has been computed, several algorithms can be used to compute either the whole spectrum or part of it. In this paper, we propose an algorithm to reduce any symmetric matrix into a similar semiseparable one of semiseparability rank 1, by orthogonal...