Linear approximation

About: Linear approximation is a research topic. Over the lifetime, 3901 publications have been published within this topic receiving 74764 citations.

Model reduction of time-varying linear systems using approximate multipoint Krylov-subspace projectors

Abstract: A method is presented for model reduction of systems described by time varying differential algebraic equations. This method allows automated extraction of reduced models for nonlinear RF blocks, such as mixers and filters, that have a near linear signal path but may contain strongly nonlinear time varying components. The models have the accuracy of a transistor level nonlinear simulation, but are very compact and so can be used in system level simulation and design. The model reduction procedure is based on a multipoint rational approximation algorithm formed by orthogonal projection of the original time varying linear system into an approximate Krylov subspace. The models obtained from the approximate Krylov subspace projector can be obtained much more easily than the exact projectors but show negligible difference in accuracy.

Numerical stabilization of Biot's consolidation model by a perturbation on the flow equation

Abstract: In this paper a stabilized finite element scheme for the poroelasticity equations is proposed. This method, based on the perturbation of the flow equation, allows us to use continuous piecewise linear approximation spaces for both displacements and pressure, obtaining solutions without oscillations independently of the chosen discretization parameters. The perturbation term depends on a parameter which is established in terms of the mesh size and the properties of the material. In the one-dimensional case, this parameter is shown to be optimal. Some numerical experiments are presented indicating the efficiency of the proposed stabilization technique. Copyright © 2008 John Wiley & Sons, Ltd.

Nonlinear Approximation and Adaptive Techniques for Solving Elliptic Operator Equations

Abstract: This survey article is concerned with two basic approximation concepts and their interrelation with the numerical solution of elliptic operator equations, namely nonlinear and adaptive approximation. On one hand, for nonlinear approximation based on wavelet expansions, the best possible approximation rate which a function can have for a given number of degrees of freedom is characterized in terms of its regularity in a certain scale of Besov spaces. Therefore, after demonstrating the gain of nonlinear approximation over linear approximation measured in a Sobolev scale, we review some recent results on the Sobolev and Besov regularity of solutions to elliptic boundary value problems. On the other hand, nonlinear approximation requires information that is generally not available in practice. Instead one has to resort to the concept of adaptive approximation. We briefly summarize some recent results on wavelet based adaptive schemes for elliptic operator equations. In contrast to more conventional approaches one can show that these schemes converge without prior assumptions on the solution, such as the saturation property. One central objective of this paper is to contribute to interrelating nonlinear approximation and adaptive methods in the context of elliptic operator equations.

On stability by the first approximation for discrete systems

Abstract: The problem of stability by the first approximation for discrete systems is considered. The Malkin-Massera-Chetaev theorem on stability by the first approximation is extended to discrete systems. The stability conditions by the first approximation for cascade are obtained