Two-sided estimation of linear approximation error second - order hypersurfaces

Linear preservers of two-sided matrix majorization

For vectors X, <span style="fon...

First and Second Order Perturbations of Hypersurfaces

In this paper we find the first and second order perturbations of the induced metric and the extrinsic curvature of a non-degenerate hypersurface Σ in a spacetime (M, g), when the metric g is perturbed arbitrarily to second order and the hypersurface itself is allowed to change perturbatively (i.e. to move within spacetime) also to second order. The results are fully general and hold in arbitra...

One - sided Versus Two - sided Error in

Second order H2 optimal approximation of linear dynamical systems

In this paper we consider the H2 optimal model reduction problem which has important applications in system approximation and has received considerable attention in the literature. An important link between special cases of this problem and rational interpolation using Krylov subspace projection methods has been recently established. We use this link to derive a solution of the second order opt...

On the stability of linear differential equations of second order

The aim of this paper is to investigate the Hyers-Ulam stability of the  linear differential equation$$y''(x)+alpha y'(x)+beta y(x)=f(x)$$in general case, where $yin C^2[a,b],$  $fin C[a,b]$ and $-infty