We consider a class of random banded Hessenberg matrices with independent entries having identical distributions along diagonals. The may be different for belonging to For sequence $$n\times n$$ in the considered, we investigate asymptotic behavior their empirical spectral distribution as n tends infinity.

Nikishin systems of three functions are considered. For such systems, the rate of convergence of simultaneous interpolating rational approximations with partially prescribed poles is studied. The solution is described in terms of the solution of a vector equilibrium problem in the presence of a vector external field.

This paper proposes an accurate and computationally efficient solver of the heat equation (∂t +D)F(·, t) = 0, F(·,0) = f , on a volumetric domain, through the (r,r)-degree Padé-Chebyshev rational approximation of the exponential representation F(·, t) = exp( tD) f of the solution. To this end, the heat diffusion problem is converted to a set of r differential equations, which involve only the L...

1. E. P. Merkes & W. T. Scott, "Continued fraction solutions of the Riccati equation," J. Math. Anal. Appl., v. 4, 1962, pp. 309-327. MR 25 #4167. 2. W. Fair, "Padé Approximations to the Solution of the Riccati Equation," Math. Comp., v. 18, 1964, pp. 627-634. MR 29 #6630. 3. Y. L. Luke, "The Padé table and the r-method," J. Math, and Phys., v. 37, 1958, pp. 110-127. MR 20 #5558. 4. H. T. Davis...

Simplified theories governing behavior of beams and plates keeping the fundamental characteristics of the being modeled objects are proposed and discussed. By simplification, we mean decrease of order of partial differential equations (PDEs) with respect to spatial coordinates. Our approach is used for both discrete and continuous models. An advantage of Padé approximation is addressed. First p...

Recently it has been pointed out that diagonal Padé approximants to truncated perturbative series in gauge theories have the remarkable property of being independent of the choice of the renormalization scale as long as the gauge coupling parameter α(p2) is taken to evolve according to the one-loop renormalization group equation – i.e., in the large-β0 approximation. In this letter we propose a...

Behavioral models are used for top-down design and for bottom-up verification. The efficient simulation of large–scale dynamical system needs a systematic procedure for order reduction of the original circuit. A method based on the moment matching for behavioral model generation of analog integrated circuits and by comparison some approaches to obtain an accurate approximation of the circuit fu...

Through considering a large scale single-input, single-output dynamical linear system, we are led to the task of finding a suitable reduced-order model corresponding to that system. Equivalently, we need to successfully approximate the system’s so-called transfer function. To approximate the transfer function the PVL method considers the Lanczos process and its close knit connection to Padé app...