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Acta Numerica 2010: Volume 19
A high-impact, prestigious, annual publication containing invited surveys by subject leaders: essential reading for all practitioners and researchers.
Mathematics of Wave Phenomena
Wave phenomena are ubiquitous in nature. Their mathematical modeling, simulation and analysis lead to fascinating and challenging problems in both analysis and numerical mathematics. These challenges and their impact on significant applications have inspired major results and methods about wave-type equations in both fields of mathematics. The Conference on Mathematics of Wave Phenomena 2018 held in Karlsruhe, Germany, was devoted to these topics and attracted internationally renowned experts from a broad range of fields. These conference proceedings present new ideas, results, and techniques from this exciting research area.
Wave Phenomena
This book presents the notes from the seminar on wave phenomena given in 2019 at the Mathematical Research Center in Oberwolfach. The research on wave-type problems is a fascinating and emerging field in mathematical research with many challenging applications in sciences and engineering. Profound investigations on waves require a strong interaction of several mathematical disciplines including functional analysis, partial differential equations, mathematical modeling, mathematical physics, numerical analysis, and scientific computing. The goal of this book is to present a comprehensive introduction to the research on wave phenomena. Starting with basic models for acoustic, elastic, and electro-magnetic waves, topics such as the existence of solutions for linear and some nonlinear material laws, efficient discretizations and solution methods in space and time, and the application to inverse parameter identification problems are covered. The aim of this book is to intertwine analysis and numerical mathematics for wave-type problems promoting thus cooperative research projects in this field.
Numerical Mathematics and Advanced Applications ENUMATH 2017
This book collects many of the presented papers, as plenary presentations, mini-symposia invited presentations, or contributed talks, from the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) 2017. The conference was organized by the University of Bergen, Norway from September 25 to 29, 2017. Leading experts in the field presented the latest results and ideas in the designing, implementation, and analysis of numerical algorithms as well as their applications to relevant, societal problems. ENUMATH is a series of conferences held every two years to provide a forum for discussing basic aspects and new trends in numerical mathematics and scientific and industrial applications. These discussions are upheld at the highest level of international expertise. The first ENUMATH conference was held in Paris in 1995 with successive conferences being held at various locations across Europe, including Heidelberg (1997), Jyvaskyla (1999), lschia Porto (2001), Prague (2003), Santiago de Compostela (2005), Graz (2007), Uppsala (2009), Leicester (2011), Lausanne (2013), and Ankara (2015).
Matrix Functions and Matrix Equations
Matrix functions and matrix equations are widely used in science, engineering and social sciences due to the succinct and insightful way in which they allow problems to be formulated and solutions to be expressed. This book covers materials relevant to advanced undergraduate and graduate courses in numerical linear algebra and scientific computing. It is also well-suited for self-study. The broad content makes it convenient as a general reference to the subjects. Contents:Matrix Functions: A Short Course (Nicholas J Higham and Lijing Lin)A Short Course on Exponential Integrators (Marlis Hochbruck)Matrix Equations and Model Reduction (Peter Benner, Tobias Breiten and Lihong Feng)Rayleigh Quot...
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016
This book features a selection of high-quality papers chosen from the best presentations at the International Conference on Spectral and High-Order Methods (2016), offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.
Computational Molecular Dynamics: Challenges, Methods, Ideas
On May 21-24, 1997 the Second International Symposium on Algorithms for Macromolecular Modelling was held at the Konrad Zuse Zentrum in Berlin. The event brought together computational scientists in fields like biochemistry, biophysics, physical chemistry, or statistical physics and numerical analysts as well as computer scientists working on the advancement of algorithms, for a total of over 120 participants from 19 countries. In the course of the symposium, the speakers agreed to produce a representative volume that combines survey articles and original papers (all refereed) to give an impression of the present state of the art of Molecular Dynamics. The 29 articles of the book reflect the main topics of the Berlin meeting which were i) Conformational Dynamics, ii) Thermodynamic Modelling, iii) Advanced Time-Stepping Algorithms, iv) Quantum-Classical Simulations and Fast Force Field and v) Fast Force Field Evaluation.
Functions of Matrices
“This superb book is timely and is written with great attention paid to detail, particularly in its referencing of the literature. The book has a wonderful blend of theory and code (MATLAB®) so will be useful both to nonexperts and to experts in the field.” — Alan Laub, Professor, University of California, Los Angeles The only book devoted exclusively to matrix functions, this research monograph gives a thorough treatment of the theory of matrix functions and numerical methods for computing them. The author's elegant presentation focuses on the equivalent definitions of f(A) via the Jordan canonical form, polynomial interpolation, and the Cauchy integral formula, and features an empha...
Linear Algebra, Rational Approximation and Orthogonal Polynomials
Evolving from an elementary discussion, this book develops the Euclidean algorithm to a very powerful tool to deal with general continued fractions, non-normal Padé tables, look-ahead algorithms for Hankel and Toeplitz matrices, and for Krylov subspace methods. It introduces the basics of fast algorithms for structured problems and shows how they deal with singular situations. Links are made with more applied subjects such as linear system theory and signal processing, and with more advanced topics and recent results such as general bi-orthogonal polynomials, minimal Padé approximation, polynomial root location problems in the complex plane, very general rational interpolation problems, an...
Krylov Methods for Nonsymmetric Linear Systems
This book aims to give an encyclopedic overview of the state-of-the-art of Krylov subspace iterative methods for solving nonsymmetric systems of algebraic linear equations and to study their mathematical properties. Solving systems of algebraic linear equations is among the most frequent problems in scientific computing; it is used in many disciplines such as physics, engineering, chemistry, biology, and several others. Krylov methods have progressively emerged as the iterative methods with the highest efficiency while being very robust for solving large linear systems; they may be expected to remain so, independent of progress in modern computer-related fields such as parallel and high perf...
