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Multigrid Methods
Multigrid methods are among the most efficient iterative methods for the solution of linear systems which arise in many large scale scientific calculations. Every researcher working with the numerical solution of partial differential equations should at least be familiar with this powerful technique. This invaluable book presents results concerning the rates of convergence of multigrid iterations.
The Theory of Quantaloids
This book presents a detailed account of the theory of quantaloids, a natural generalization of quantales. The basic theory, examples and construction are given and particular emphasis is placed on the free quantaloid construction, as well as on the perspective provided by enriched categories.
Conjugate Gradient Type Methods for Ill-Posed Problems
The conjugate gradient method is a powerful tool for the iterative solution of self-adjoint operator equations in Hilbert space.This volume summarizes and extends the developments of the past decade concerning the applicability of the conjugate gradient method (and some of its variants) to ill posed problems and their regularization. Such problems occur in applications from almost all natural and technical sciences, including astronomical and geophysical imaging, signal analysis, computerized tomography, inverse heat transfer problems, and many more This Research Note presents a unifying analysis of an entire family of conjugate gradient type methods. Most of the results are as yet unpublish...
Partial Differential Equations On Multistructures
This text is based on lectures presented at the International Conference on Partial Differential Equations (PDEs) on Multistructures, held in Luminy, France. It contains advances in the field, compiling research on the analyses and applications of multistructures - including treatments of classical theories, specific characterizations and modellings of multistructures, and discussions on uses in physics, electronics, and biology.
Analysis and Applications
Analysis and its applications have been major areas for research in mathematics and allied fields. The fast growing power of computation has made a significant and useful impact in these areas. This has lead to computational analysis and the emergence of fields like Bezier-Bernstein methods for computer-aided geometric design, constructive approximation and wavelets, and even computational harmonic analysis. Analysis and Applications consists of research articles, including a few survey articles, by eminent mathematicians projecting trends in constructive and computational approximation, summability theory, optimal control and theory and applications of function spaces and wavelets.
Topics in the Mathematical Modelling of Composite Materials
Over the past several decades, we have witnessed a renaissance of theoretical work on the macroscopic behavior of microscopically heterogeneous materials. This activity brings together a number of related themes, including: (1) the use of weak convergence as a rigorous yet general language for the discussion of macroscopic behavior; (2) interest in new types of questions, particularly the "G-closure problem," motivated in large part by applications of optimal control theory to structural optimization; (3) the introduction of new methods for bounding effective moduli, including one based on "compensated compactness"; and (4) the identification of deep links between the analysis of microstruct...
Trends in Industrial and Applied Mathematics
This book contains current results of research on numerical solutions of Schrodinger-type problems, sampling theorems, numerical methods for large-scale non-convex quadratic programming, derivative-free algorithms, free material optimization, Moreau's sweeping process and a perspective on industrial mathematics work in recent years. The book also includes wavelet-based digital watermarking techniques and computer simulation of meteorological parameters. One chapter of the book is also devoted to the importance of strange attractors for industrial mathematics. Audience: Academic researchers, as well as researchers working in industry.
Numerical Analysis 1995
This volume contains invited papers presented at the 16th Dundee Biennial Conference on Numerical Analysis held at the University of Dundee, 27-30 June, 1995. The Dundee Conferences are important events in the numerical analysis calendar, and the thirteen papers published here represent accounts of recent research work by leading numerical analysts covering a wide range of fields of interest. The book is a valuable guide to the direction of current research in many areas of numerical analysis. It will be of particular interest to graduate students and research workers concerned with the theory and application of numerical methods for solving ordinary and partial differential equations, with emphasis on problems in fluid dynamics. It also contains contributions to research into methods of linear algebra, numerical methods for optimisation problems and surface fitting.
Elliptic Operators, Topology, and Asymptotic Methods, Second Edition
Ten years after publication of the popular first edition of this volume, the index theorem continues to stand as a central result of modern mathematics-one of the most important foci for the interaction of topology, geometry, and analysis. Retaining its concise presentation but offering streamlined analyses and expanded coverage of important examples and applications, Elliptic Operators, Topology, and Asymptotic Methods, Second Edition introduces the ideas surrounding the heat equation proof of the Atiyah-Singer index theorem. The author builds towards proof of the Lefschetz formula and the full index theorem with four chapters of geometry, five chapters of analysis, and four chapters of top...
Elliptic Operators, Topology, and Asymptotic Methods
Ten years after publication of the popular first edition of this volume, the index theorem continues to stand as a central result of modern mathematics-one of the most important foci for the interaction of topology, geometry, and analysis. Retaining its concise presentation but offering streamlined analyses and expanded coverage of important exampl
