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Numerical Methods for General and Structured Eigenvalue Problems
This book is about computing eigenvalues, eigenvectors, and invariant subspaces of matrices. Treatment includes generalized and structured eigenvalue problems and all vital aspects of eigenvalue computations. A unique feature is the detailed treatment of structured eigenvalue problems, providing insight on accuracy and efficiency gains to be expected from algorithms that take the structure of a matrix into account.
Exploiting Hidden Structure in Matrix Computations: Algorithms and Applications
Focusing on special matrices and matrices which are in some sense `near’ to structured matrices, this volume covers a broad range of topics of current interest in numerical linear algebra. Exploitation of these less obvious structural properties can be of great importance in the design of efficient numerical methods, for example algorithms for matrices with low-rank block structure, matrices with decay, and structured tensor computations. Applications range from quantum chemistry to queuing theory. Structured matrices arise frequently in applications. Examples include banded and sparse matrices, Toeplitz-type matrices, and matrices with semi-separable or quasi-separable structure, as well as Hamiltonian and symplectic matrices. The associated literature is enormous, and many efficient algorithms have been developed for solving problems involving such matrices. The text arose from a C.I.M.E. course held in Cetraro (Italy) in June 2015 which aimed to present this fast growing field to young researchers, exploiting the expertise of five leading lecturers with different theoretical and application perspectives.
The Matrix Eigenvalue Problem
The first in-depth, complete, and unified theoretical discussion of the two most important classes of algorithms for solving matrix eigenvalue problems: QR-like algorithms for dense problems and Krylov subspace methods for sparse problems. The author discusses the theory of the generic GR algorithm, including special cases (for example, QR, SR, HR), and the development of Krylov subspace methods. This book also addresses a generic Krylov process and the Arnoldi and various Lanczos algorithms, which are obtained as special cases. Theoretical and computational exercises guide students, step by step, to the results. Downloadable MATLAB programs, compiled by the author, are available on a supplementary Web site. Readers of this book are expected to be familiar with the basic ideas of linear algebra and to have had some experience with matrix computations. Ideal for graduate students, or as a reference book for researchers and users of eigenvalue codes.
Numerical Mathematics and Advanced Applications - ENUMATH 2013
This book gathers a selection of invited and contributed lectures from the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) held in Lausanne, Switzerland, August 26-30, 2013. It provides an overview of recent developments in numerical analysis, computational mathematics and applications from leading experts in the field. New results on finite element methods, multiscale methods, numerical linear algebra and discretization techniques for fluid mechanics and optics are presented. As such, the book offers a valuable resource for a wide range of readers looking for a state-of-the-art overview of advanced techniques, algorithms and results in numerical mathematics and scientific computing.
Euro-Par 2019: Parallel Processing
This book constitutes the proceedings of the 25th International Conference on Parallel and Distributed Computing, Euro-Par 2019, held in Göttingen, Germany, in August 2019. The 36 full papers presented in this volume were carefully reviewed and selected from 142 submissions. They deal with parallel and distributed computing in general, focusing on support tools and environments; performance and power modeling, prediction and evaluation; scheduling and load balancing; high performance architectures and compilers; data management, analytics and deep learning; cluster and cloud computing; distributed systems and algorithms; parallel and distributed programming, interfaces, and languages; multicore and manycore parallelism; theory and algorithms for parallel computation and networking; parallel numerical methods and applications; accelerator computing; algorithms and systems for bioinformatics; and algorithms and systems for digital humanities.
Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory
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 algebra (his first full professorship at TU Chemnitz was in "Numerical Algebra," hence the title of the book) and mat...
Parallel Processing and Applied Mathematics, Part I
Annotation This book constitutes the proceedings of the 8th International Conference on Parallel Processing and Applied Mathematics, PPAM 2009, held in Wroclaw, Poland, in September 2009.
Photogrammetric Image Analysis
This book constitutes the refereed proceedings of the ISPRS Conference on Photogrammetric Image Analysis, held in Munich, Germany, in October 2011. The 25 revised full papers presented were carefully reviewed and selected from 54 submissions. The papers are organized in topical sections on orientation, matching, object detection, 3D reconstruction and DEM, classification, people and tracking, as well as image processing.
Bits and Bugs
In scientific computing (also known as computational science), advanced computing capabilities are used to solve complex problems. This self-contained book describes and analyzes reported software failures related to the major topics within scientific computing: mathematical modeling of phenomena; numerical analysis (number representation, rounding, conditioning); mathematical aspects and complexity of algorithms, systems, or software; concurrent computing (parallelization, scheduling, synchronization); and numerical data (such as input of data and design of control logic). Readers will find lists of related, interesting bugs, MATLAB examples, and ?excursions? that provide necessary background, as well as an in-depth analysis of various aspects of the selected bugs. Illustrative examples of numerical principles such as machine numbers, rounding errors, condition numbers, and complexity are also included. ?
Applied Parallel and Scientific Computing
The two volume set LNCS 7133 and LNCS 7134 constitutes the thoroughly refereed post-conference proceedings of the 10th International Conference on Applied Parallel and Scientific Computing, PARA 2010, held in Reykjavík, Iceland, in June 2010. These volumes contain three keynote lectures, 29 revised papers and 45 minisymposia presentations arranged on the following topics: cloud computing, HPC algorithms, HPC programming tools, HPC in meteorology, parallel numerical algorithms, parallel computing in physics, scientific computing tools, HPC software engineering, simulations of atomic scale systems, tools and environments for accelerator based computational biomedicine, GPU computing, high performance computing interval methods, real-time access and processing of large data sets, linear algebra algorithms and software for multicore and hybrid architectures in honor of Fred Gustavson on his 75th birthday, memory and multicore issues in scientific computing - theory and praxis, multicore algorithms and implementations for application problems, fast PDE solvers and a posteriori error estimates, and scalable tools for high performance computing.
