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Complex Interval Arithmetic and Its Applications
The aim of this book is to present formulas and methods developed using complex interval arithmetic. While most of numerical methods described in the literature deal with real intervals and real vectors, there is no systematic study of methods in complex interval arithmetic. The book fills this gap. Several main subjects are considered: outer estimates for the range of complex functions, especially complex centered forms, the best approximations of elementary complex functions by disks, iterative methods for the inclusion by polynomial zeros including their implementation on parallel computers, the analysis of numerical stability of iterative methods by using complex interval arithmetic and numerical computation of curvilinear integrals with error bounds. Mainly new methods are presented developed over the last years, including a lot of very recent results by the authors some of which have not been published before.
Differential Equations, Asymptotic Analysis, and Mathematical Physics
This volume contains a collection of original papers, associated with the International Conference on Partial Differential Equations, held in Potsdam, July 29 to August 2, 1996. The conference has taken place every year on a high scientific level since 1991; this event is connected with the activities of the Max Planck Research Group for Partial Differential Equations at Potsdam. Outstanding researchers and specialists from Armenia, Belarus, Belgium, Bulgaria, Canada, China, France, Germany, Great Britain, India, Israel, Italy, Japan, Poland, Romania, Russia, Spain, Sweden, Switzerland, Ukraine, and the USA contribute to this volume. The main topics concern recent progress in partial differential equations, microlocal analysis, pseudo-differential operators on manifolds with singularities, aspects in differential geometry and index theory, operator theory and operator algebras, stochastic spectral analysis, semigroups, Dirichlet forms, Schrodinger operators, semiclassical analysis, and scattering theory.
Parcella '94
The Parcella series is a forum for displaying the landscape of research in East European countries and is also a meeting place for exchanging ideas and initiating steps towards a future of broad scoped East-West co-operation in a unified Europe. Advanced supercomputing and the obtained software technology are of great importance for the East-West technological co-operation. It includes applications like energy and raw material resources planning and exploration modelling, material research (special metals, ceramics, semiconductors) and industrial supercomputing. These proceedings contain several recent research results on the topics of mathematical foundations of parallel computing, languages, programming, theory of algorithms, data flow, design of architectures and systems, memory and memory access, interconnection networks, routing, image processing and modelling, computational geometry, computer graphics, graphalgorithms, fault-tolerant computing, neurocomputing and connectionism, optical computing, scientific computation, applications in biology, physics, engineering, manufacturing systems, program packages and problem solving environments supporting scientific computations.
Parcella '96
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Partial Differential Equations
This volume contains the contributions of the conference "Partial Differential Equations" in Han-sur-Lesse, Belgium, December 1993. The originally intended Belgian-French meeting developed into a truely international conference, including specialists from Argentina, Germany, Puerto Rico, Russia, Spain, and the USA. The authors was to discuss a variety of important questions in applied sciences, engineering and mathematical physics which lead to deep structures and new challenges to the analysis of partial differential equations. The articles show the complexity of phenomena for a broader readership in non-linear analysis, free boundary value problems, effects from singularities, asymptotics, and stability of solutions.
Uncertainty
Uncertainty influences the individual as well as society; so it is important to enhance our understanding of uncertainty. First of all, do we all agree on a unique definition of uncertainty in the natural and technological worlds? Secondly, how can we model uncertainty? Is it purely a state of mind, the lack of complete knowledge, or is it a phenomenon in its own right? What heuristic and mathematical models are available? What types of questions about uncertainty can be formulated? What questions can be realistically answered? Do scholars in diverse fields agree on these issues? These and other questions are addressed by 20 scholars from mechanical, civil, electrical, material, aerospace and ocean engineering, from applied mathematics, economics, industrial engineering and operations research, control theory, geodesy, systems science, and philosophy.
Numerical Methods and Error Bounds
This volume contains the invited talks and short communications presented at the IMACS-GAMM International Symposium. The participants from all over the world presented their results in the field of development and investigation of numerical algorithms under the aspect of constructing proper error bounds for approximated solutions. Among the subjects of the talks were problems like systems of linear and nonlinear equations,ordinary and partial differential equation solvers, data fitting methods, computer geometry, computer arithmetic, interval arithmetic, and selected problems in theoretical mechanics.
Approximation Theory
This volume contains the contributions of the International Dortmund Meeting on Approximation Theory (IDoMAT 95) at Haus Bommerholz the conference center of Dortmund University during the week of March 13-17, 1995. At this international conference researchers and specialists from China, England, France, Hungary, Israel, Italy, Romania, U.S.A. and Germany described new developments in the fields of approximation theory. The authors discuss a variety of important ideas, questions and applicable methods in applied sciences and in several fields of approximation theory which lead to new challenges to the approximation by means of linear operators and shape preserving approximation, methods for the study of differential (diffusion) equations, approximation results of solutions of specific hyperbolic differential equations, polynomial and spline interpolation, density problems in multivariate approximation, orthogonal polynomials and wavelets. This volume collects the complete papers of the invited lectures together with a selection of papers relating to the research talks presented at IDoMAT 95.
