Download or read book Hierarchical Matrices Algorithms and Analysis written by Wolfgang Hackbusch and published by Springer. This book was released on 2015-12-21 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained monograph presents matrix algorithms and their analysis. The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g., the matrix exponential. Other applications include the solution of matrix equations, e.g., the Lyapunov or Riccati equation. The required mathematical background can be found in the appendix. The numerical treatment of fully populated large-scale matrices is usually rather costly. However, the technique of hierarchical matrices makes it possible to store matrices and to perform matrix operations approximately with almost linear cost and a controllable degree of approximation error. For important classes of matrices, the computational cost increases only logarithmically with the approximation error. The operations provided include the matrix inversion and LU decomposition. Since large-scale linear algebra problems are standard in scientific computing, the subject of hierarchical matrices is of interest to scientists in computational mathematics, physics, chemistry and engineering.
Download or read book Matrix Preconditioning Techniques and Applications written by Ke Chen and published by Cambridge University Press. This book was released on 2005-07-14 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to preconditioning techniques, now an essential part of successful and efficient iterative solutions of matrices.
Download or read book Hierarchical Matrices written by Mario Bebendorf and published by Springer Science & Business Media. This book was released on 2008-06-25 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hierarchical matrices are an efficient framework for large-scale fully populated matrices arising, e.g., from the finite element discretization of solution operators of elliptic boundary value problems. In addition to storing such matrices, approximations of the usual matrix operations can be computed with logarithmic-linear complexity, which can be exploited to setup approximate preconditioners in an efficient and convenient way. Besides the algorithmic aspects of hierarchical matrices, the main aim of this book is to present their theoretical background. The book contains the existing approximation theory for elliptic problems including partial differential operators with nonsmooth coefficients. Furthermore, it presents in full detail the adaptive cross approximation method for the efficient treatment of integral operators with non-local kernel functions. The theory is supported by many numerical experiments from real applications.
Download or read book Multilevel Block Factorization Preconditioners written by Panayot S. Vassilevski and published by Springer Science & Business Media. This book was released on 2008-10-22 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is the first to provide a comprehensive, self-contained and rigorous presentation of some of the most powerful preconditioning methods for solving finite element equations in a common block-matrix factorization framework. The book covers both algorithms and analysis using a common block-matrix factorization approach which emphasizes its unique feature. Topics covered include the classical incomplete block-factorization preconditioners, the most efficient methods such as the multigrid, algebraic multigrid, and domain decomposition. This text can serve as an indispensable reference for researchers, graduate students, and practitioners. It can also be used as a supplementary text for a topics course in preconditioning and/or multigrid methods at the graduate level.
Download or read book Algorithms for Sparse Linear Systems written by Jennifer Scott and published by Springer Nature. This book was released on 2023-04-29 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Large sparse linear systems of equations are ubiquitous in science, engineering and beyond. This open access monograph focuses on factorization algorithms for solving such systems. It presents classical techniques for complete factorizations that are used in sparse direct methods and discusses the computation of approximate direct and inverse factorizations that are key to constructing general-purpose algebraic preconditioners for iterative solvers. A unified framework is used that emphasizes the underlying sparsity structures and highlights the importance of understanding sparse direct methods when developing algebraic preconditioners. Theoretical results are complemented by sparse matrix algorithm outlines. This monograph is aimed at students of applied mathematics and scientific computing, as well as computational scientists and software developers who are interested in understanding the theory and algorithms needed to tackle sparse systems. It is assumed that the reader has completed a basic course in linear algebra and numerical mathematics.
Download or read book SIAM Journal on Scientific Computing written by and published by . This book was released on 2008 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Robust Algebraic Multilevel Methods and Algorithms written by Johannes Kraus and published by Walter de Gruyter. This book was released on 2009-09-04 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with algorithms for the solution of linear systems of algebraic equations with large-scale sparse matrices, with a focus on problems that are obtained after discretization of partial differential equations using finite element methods. The authors provide a systematic presentation of the recent advances in robust algebraic multilevel methods and algorithms, e.g., the preconditioned conjugate gradient method, algebraic multilevel iteration (AMLI) preconditioners, the classical algebraic multigrid (AMG) method and its recent modifications, namely AMG using element interpolation (AMGe) and AMG based on smoothed aggregation. The first six chapters can serve as a short introductory course on the theory of AMLI methods and algorithms. The next part of the monograph is devoted to more advanced topics, including the description of new generation AMG methods, AMLI methods for discontinuous Galerkin systems, looking-free algorithms for coupled problems etc., ending with important practical issues of implementation and challenging applications. This second part is addressed to some more experienced students and practitioners and can be used to complete a more advanced course on robust AMLI and AMG methods and their efficient application. This book is intended for mathematicians, engineers, natural scientists etc.
Download or read book Acta Numerica 2005 Volume 14 written by Arieh Iserles and published by Cambridge University Press. This book was released on 2005-06-30 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: A high-impact factor, prestigious annual publication containing invited surveys by subject leaders: essential reading for all practitioners and researchers.
Download or read book Numerical Approximation Methods for Elliptic Boundary Value Problems written by Olaf Steinbach and published by Springer Science & Business Media. This book was released on 2007-11-26 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unified theory of the Finite Element Method and the Boundary Element Method for a numerical solution of second order elliptic boundary value problems. This includes the solvability, stability, and error analysis as well as efficient methods to solve the resulting linear systems. Applications are the potential equation, the system of linear elastostatics and the Stokes system. While there are textbooks on the finite element method, this is one of the first books on Theory of Boundary Element Methods. It is suitable for self study and exercises are included.
Download or read book High Performance Scientific Computing written by Michael W. Berry and published by Springer Science & Business Media. This book was released on 2012-01-18 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the state of the art in parallel numerical algorithms, applications, architectures, and system software. The book examines various solutions for issues of concurrency, scale, energy efficiency, and programmability, which are discussed in the context of a diverse range of applications. Features: includes contributions from an international selection of world-class authorities; examines parallel algorithm-architecture interaction through issues of computational capacity-based codesign and automatic restructuring of programs using compilation techniques; reviews emerging applications of numerical methods in information retrieval and data mining; discusses the latest issues in dense and sparse matrix computations for modern high-performance systems, multicores, manycores and GPUs, and several perspectives on the Spike family of algorithms for solving linear systems; presents outstanding challenges and developing technologies, and puts these in their historical context.
Download or read book Large Scale Scientific Computing written by Ivan Lirkov and published by Springer Science & Business Media. This book was released on 2006-02-14 with total page 701 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-proceedings of the 5th International Conference on Large-Scale Scientific Computations, LSSC 2005, held in Sozopol, Bulgaria in June 2005. The 75 revised full papers presented together with five invited papers were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections.
Download or read book Parallel Computational Technologies written by Leonid Sokolinsky and published by Springer Nature. This book was released on 2022-07-18 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 16th International Conference on Parallel Computational Technologies, PCT 2022, held in Dubna, Russia, during March 29–31, 2022. The 22 full papers included in this book were carefully reviewed and selected from 60 submissions. They were organized in topical sections as follows: high performance architectures, tools and technologies; parallel numerical algorithms; supercomputer simulation.
Download or read book Boundary Element Analysis written by Martin Schanz and published by Springer Science & Business Media. This book was released on 2007-04-29 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains eleven contributions on boundary integral equation and boundary element methods. Beside some historical and more analytical aspects in the formulation and analysis of boundary integral equations, modern fast boundary element methods are also described and analyzed from a mathematical point of view. In addition, the book presents engineering and industrial applications that show the ability of boundary element methods to solve challenging problems from different fields.
Download or read book A Journey through the History of Numerical Linear Algebra written by Claude Brezinski and published by SIAM. This book was released on 2022-12-06 with total page 813 pages. Available in PDF, EPUB and Kindle. Book excerpt: This expansive volume describes the history of numerical methods proposed for solving linear algebra problems, from antiquity to the present day. The authors focus on methods for linear systems of equations and eigenvalue problems and describe the interplay between numerical methods and the computing tools available at the time. The second part of the book consists of 78 biographies of important contributors to the field. A Journey through the History of Numerical Linear Algebra will be of special interest to applied mathematicians, especially researchers in numerical linear algebra, people involved in scientific computing, and historians of mathematics.
Download or read book Numerical Analysis and Its Applications written by Svetozar D. Margenov and published by Springer. This book was released on 2009-02-07 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 4th International Conference on Numerical Analysis and Its Applications, NAA 2008, held in Lozenetz, Bulgaria in June 2008. The 61 revised full papers presented together with 13 invited papers were carefully selected during two rounds of reviewing and improvement. The papers address all current aspects of numerical analysis and discuss a wide range of problems concerning recent achievements in physics, chemistry, engineering, and economics. A special focus is given to numerical approximation and computational geometry, numerical linear algebra and numerical solution of transcendental equations, numerical methods for differential equations, numerical modeling, and high performance scientific computing.
Download or read book Automated Practical Reasoning written by Jochen Pfalzgraf and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of selected papers written by researchers qf our "RISC" institute (Research Institute for Symbolic Computation) along with the ESPRIT MEDLAR Project (Mechanizing Deduction in the Logics of Practical Reason ing). Naturally, the MEDLAR Project was and is the focal point for our institute whose main objective is the combination of foundational research in the area of symbolic computation and possible applications thereof for high-tech industrial projects. I am grateful to the director of the MEDLAR project, Jim Cunningham, for his enthusiasm, profound expertise, and continuous effort to manage a fruitful cooperation between various European working groups in the area of the project and for giving us the opportunity to be part of this challenging endeavor. I also acknowledge and feel indebted to Jochen Pfalzgraf for managing the RISC part of the MEDLAR project and to both him and Dongming Wang for editing this volume and organizing the refereeing process.
Download or read book Multigrid Methods II written by Wolfgang Hackbusch and published by Lecture Notes in Mathematics. This book was released on 1986-12 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:
