Kategoria BISAC: Mathematics >> Number Systems

This edited volume highlights the scientific contributions of Volker Mehrmann, a leading expert in the area of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory. These mathematical research areas are strongly related and often occur in the same real-world applications. The main areas where such applications emerge are computational engineering and sciences, but increasingly also social sciences and economics.

This book also reflects some of Volker Mehrmann's major career stages. Starting out working in the areas of numerical linear...

This book is about numerical modeling of multiscale problems, and introduces several asymptotic analysis and numerical techniques which are necessary for a proper approximation of equations that depend on different physical scales. Aimed at advanced undergraduate and graduate students in mathematics, engineering and physics or researchers seeking a no-nonsense approach, it discusses examples in their simplest possible settings, removing mathematical hurdles that might hinder a clear understanding of the methods.

The problems considered are given by singular perturbed reaction...

Based on their research experience, the authors propose a reference textbook in two volumes on the theory of generalized locally Toeplitz sequences and their applications. This first volume focuses on the univariate version of the theory and the related applications in the unidimensional setting, while the second volume, which addresses the multivariate case, is mainly devoted to concrete PDE applications.

Computational Methods for Numerical Analysis with R is an overview of traditional numerical analysis topics presented using R. This guide shows how common functions from linear algebra, interpolation, numerical integration, optimization, and differential equations can be implemented in pure R code. Every algorithm described is given with a complete function implementation in R, along with examples to demonstrate the function and its use.

Computational Methods for Numerical Analysis with R is intended for those who already know R, but are interested in...

In this book the Wong-Zakai approximation and Wiener chaos expansion are used for stochastic partial differential equations. In this framework, the reader is led to systems of deterministic partial differential equations with unknowns being the Wiener chaos expansion coefficients. The importance of the special structure of linear systems is emphasized. Sparse grid collocation methods are also discussed as well as generalized polynomial chaos. The advantages of the Wong-Zakai approximation are presented for stochastic ordinary and partial differential equations. Moreover, the Wick-Malliavin...

This work focuses on the preservation of attractors and saddle points of ordinary differential equations under discretisation. In the 1980s, key results for autonomous ordinary differential equations were obtained - by Beyn for saddle points and by Kloeden & Lorenz for attractors. One-step numerical schemes with a constant step size were considered, so the resulting discrete time dynamical system was also autonomous. One of the aims of this book is to present new findings on the discretisation of dissipative nonautonomous dynamical systems that have been obtained in recent years, and in...