Numerisk analyse

Dieses Buch gibt eine Einfuhrung in die mathematische und informatische Modellierung sowie in die Simulation als universelle Methodik. Und so geht es um Klassen von Modellen, um deren Herleitung und um die Vielfalt an Beschreibungsarten, die eingesetzt werden konnen - diskret oder kontinuierlich, deterministisch oder stochastisch. Aber immer geht es auch darum, wie aus unterschiedlichen abstrakten Modellen ganz konkrete Simulationsergebnisse gewonnen werden konnen. Nach einem kompakten Repetitorium zum benotigten mathematischen Apparat wird das Konzept Uber das Modell zur Simulation"e; anhand von 14 Szenarien aus den Bereichen Spielen - entscheiden - planen"e;, Verkehr auf Highways und Datenhighways"e;, Dynamische Systeme"e; sowie Physik im Rechner"e; umgesetzt. Ob Spieltheorie oder Finanzmathematik, Verkehr oder Regelung, ob Populationsdynamik oder Chaos, Molekulardynamik, Kontinuumsmechanik oder Computergraphik - der Leser erhalt auf anschauliche und doch systematische Weise Einblicke in die Welt der Modelle und Simulationen.

This book and its companion volume, LNCS vols. 7331 and 7332, constitute the proceedings of the Third International Conference on Swarm Intelligence, ICSI 2012, held in Shenzhen, China in June 2012. The 145 revised full papers presented were carefully reviewed and selected from 247 submissions. The papers are organized in 27 cohesive sections covering all major topics of swarm intelligence research and developments.

This book constitutes the refereed proceedings of the 6th International Workshop on Experimental and Efficient Algorithms, WEA 2007, held in Rome, Italy, in June 2007. The 30 revised full papers presented together with three invited talks cover the design, analysis, implementation, experimental evaluation, and engineering of efficient algorithms.

Clifford algebras are at a crossing point in a variety of research areas, including abstract algebra, crystallography, projective geometry, quantum mechanics, differential geometry and analysis. For many researchers working in this field in ma- thematics and physics, computer algebra software systems have become indispensable tools in theory and applications. This edited survey book consists of 20 chapters showing application of Clifford algebra in quantum mechanics, field theory, spinor calculations, projective geometry, Hypercomplex algebra, function theory and crystallography. Many examples of computations performed with a variety of readily available software programs are presented in detail, i.e., Maple, Mathematica, Axiom, etc. A key feature of the book is that it shows how scientific knowledge can advance with the use of computational tools and software.

This monograph presents a collection of results, observations, and examples related to dynamical systems described by linear and nonlinear ordinary differential and difference equations. In particular, dynamical systems that are susceptible to analysis by the Liapunov approach are considered. The naive observation that certain "e;diagonal-type"e; Liapunov functions are ubiquitous in the literature attracted the attention of the authors and led to some natural questions. Why does this happen so often? What are the spe- cial virtues of these functions in this context? Do they occur so frequently merely because they belong to the simplest class of Liapunov functions and are thus more convenient, or are there any more specific reasons? This monograph constitutes the authors' synthesis of the work on this subject that has been jointly developed by them, among others, producing and compiling results, properties, and examples for many years, aiming to answer these questions and also to formalize some of the folklore or "e;cul- ture"e; that has grown around diagonal stability and diagonal-type Liapunov functions. A natural answer to these questions would be that the use of diagonal- type Liapunov functions is frequent because of their simplicity within the class of all possible Liapunov functions. This monograph shows that, although this obvious interpretation is often adequate, there are many in- stances in which the Liapunov approach is best taken advantage of using diagonal-type Liapunov functions. In fact, they yield necessary and suffi- cient stability conditions for some classes of nonlinear dynamical systems.

On becoming familiar with difference equations and their close re- lation to differential equations, I was in hopes that the theory of difference equations could be brought completely abreast with that for ordinary differential equations. [HUGH L. TURRITTIN, My Mathematical Expectations, Springer Lecture Notes 312 (page 10), 1973] A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both. [E. T. BELL, Men of Mathematics, Simon and Schuster, New York (page 13/14), 1937] The theory of time scales, which has recently received a lot of attention, was introduced by Stefan Hilger in his PhD thesis [159] in 1988 (supervised by Bernd Aulbach) in order to unify continuous and discrete analysis. This book is an intro- duction to the study of dynamic equations on time scales. Many results concerning differential equations carryover quite easily to corresponding results for difference equations, while other results seem to be completely different in nature from their continuous counterparts. The study of dynamic equations on time scales reveals such discrepancies, and helps avoid proving results twice, once for differential equa- tions and once for difference equations. The general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so-called time scale, which is an arbitrary nonempty closed subset of the reals.

This book constitutes the refereed proceedings of the Third International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2006, held in Tarragona, Spain, in April 2006. The 31 revised full papers presented together with 4 invited lectures were thoroughly reviewed and selected from 97 submissions. The papers are devoted to theory and tools for modeling decisions, as well as applications that encompass decision making processes and information fusion techniques.

Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball focuses on spherical problems as they occur in the geosciences and medical imaging. It comprises the author's lectures on classical approximation methods based on orthogonal polynomials and selected modern tools such as splines and wavelets.Methods for approximating functions on the real line are treated first, as they provide the foundations for the methods on the sphere and the ball and are useful for the analysis of time-dependent (spherical) problems. The author then examines the transfer of these spherical methods to problems on the ball, such as the modeling of the Earth's or the brain's interior. Specific topics covered include:* the advantages and disadvantages of Fourier, spline, and wavelet methods* theory and numerics of orthogonal polynomials on intervals, spheres, and balls* cubic splines and splines based on reproducing kernels* multiresolution analysis using wavelets and scaling functionsThis textbook is written for students in mathematics, physics, engineering, and the geosciences who have a basic background in analysis and linear algebra. The work may also be suitable as a self-study resource for researchers in the above-mentioned fields.