The method of intermediate problems of Weinstein and Aronszajn (cf. [19, 20]) provides a means of calculation for bounds to eigenvalues complementary to the Rayleigh{Ritz bounds. Convergence theorems for the method of intermediate problems in a generality that includes problems with essential spectra can be found in [5, 7{9, 12]. This paper supplements the general convergence theorems of [7, 9]...

We study the propagation, observation and control properties of the quadratic P2classical finite element semi-discretization of the 1-d wave equation on a bounded interval. A careful Fourier analysis of the discrete wave dynamics reveals two different branches in the spectrum: the acoustic one, of physical nature, and the optic one, related to the perturbations that this secondorder finite elem...

In this paper, we present a linear time DC-Gain matched BTR (DBTR) method for the VLSI interconnect order reduction. From the circuit point of view, the original BTR has a serious drawback that the DC gain between the original and the reduced order system doesn’t match. We propose the DBTR method which can both match the DC gain and guarantee the performance of the reduced order system. Moreove...

The stability of travelling and standing rolls in oscillatory rotating convection is considered from the point of view of equivariant bifurcation theory. To study stability with respect to oblique perturbations the problem is formulated on a rotating rhombic lattice. All primary solution branches with maximal isotropy are determined together with their stability properties using a truncation of...

This paper proposes a data-driven model reduction approach on the basis of noisy data with known noise model. Firstly, concept is introduced. In particular, we show that set reduced-order models obtained by applying Petrov-Galerkin projection to all systems explaining characterized in large-dimensional quadratic matrix inequality (QMI) can again be lower-dimensional QMI. Next, develop generaliz...

In this research, a numerical algorithm is employed to investigate the classical Blasius equation which is the governing equation of boundary layer problem. The base of this algorithm is on the development of RCW (Rahmanzadeh-Cai-White) method. In fact, in the current work, an attempt is made to solve the Blasius equation by using the sum of Taylor and Fourier series. While, in the most common ...

This paper revisits modal truncation from an optimisation point of view. In particular, the concept dominant poles is formulated with respect to different system norms as solution associated optimal problem. The latter reformulated equivalent convex integer or mixed-integer program. Numerical examples highlight and approach.