Hierarchical Matrices Algorithms And Analysis
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Hierarchical Matrices Algorithms And Analysis
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Author : Wolfgang Hackbusch
language : en
Publisher:
Release Date : 2015
Hierarchical Matrices Algorithms And Analysis written by Wolfgang Hackbusch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
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.
Exploiting Hidden Structure In Matrix Computations Algorithms And Applications
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Author : Michele Benzi
language : en
Publisher: Springer
Release Date : 2017-01-24
Exploiting Hidden Structure In Matrix Computations Algorithms And Applications written by Michele Benzi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-24 with Mathematics categories.
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.
Developing Linear Algebra Codes On Modern Processors Emerging Research And Opportunities
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Author : Catalán Pallarés, Sandra
language : en
Publisher: IGI Global
Release Date : 2022-10-14
Developing Linear Algebra Codes On Modern Processors Emerging Research And Opportunities written by Catalán Pallarés, Sandra and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-14 with Mathematics categories.
Optimized linear algebra (LA) libraries that are able to exploit the underlying hardware are always of interest in the high-performance computing community. The implementation of LA software has evolved along with computer architecture, while the specification remains unaltered almost from the beginning. It is important to differentiate between the specification of LA libraries and their implementation. Because LA libraries pursue high performance, the implementation for a given architecture needs to be optimized for it specifically. However, the type of operations included in the libraries, the input/output parameters, and the data types to be handled are common to all of them. This is why, while the specification remains constant, the implementation evolves with the creation of new architectures. Developing Linear Algebra Codes on Modern Processors: Emerging Research and Opportunities presents the main characteristics of LA libraries, showing the differences between the standards for sparse and dense versions. It further explores relevant linear algebra problems and shows, in a clear and understandable way, how to solve them using different computer architectures. Covering topics such as programming models, batched computing, and distributed memory platforms, this premier reference source is an excellent resource for programmers, computer scientists, engineers, students and faculty of higher education, librarians, researchers, and academicians.
Cloud Computing Big Data And Emerging Topics
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Author : Marcelo Naiouf
language : en
Publisher: Springer Nature
Release Date : 2025-10-16
Cloud Computing Big Data And Emerging Topics written by Marcelo Naiouf and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-10-16 with Computers categories.
This book constitutes the revised selected papers of the 13th International Conference on Cloud Computing, Big Data & Emerging Topics, JCC-BD&ET 2025, held in La Plata, Argentina, during June 24-26, 2025. The 12 full papers presented were carefully reviewed and selected from 35 submissions. They were focused on topical sections as follows: Parallel and Distributed Computing; Machine and Deep Learning; Smart Cities and E-Government; Visualization; Emerging Topics and Innovation in Computer Science Education.
Optimization Discrete Mathematics And Applications To Data Sciences
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Author : Ashkan Nikeghbali
language : en
Publisher: Springer Nature
Release Date : 2025-01-08
Optimization Discrete Mathematics And Applications To Data Sciences written by Ashkan Nikeghbali and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-08 with Mathematics categories.
This book delves into the dynamic intersection of optimization and discrete mathematics, offering a comprehensive exploration of their applications in data sciences. Through a collection of high-quality papers, readers will gain insights into cutting-edge research and methodologies that address complex problems across a wide array of topics. The chapters cover an impressive range of subjects, including advances in the study of polynomials, combinatorial identities, and global optimization algorithms. Readers will encounter innovative approaches to predictive models for non-performing loans, rainbow greedy matching algorithms, and the cost of detection in interaction testing. The book also examines critical issues such as demand aggregation, mid-term energy planning, and minimum-cost energy flow. Contributions from expert authors provide a deep dive into multilevel low-rank matrices, the protection of medical image authenticity, and the mathematical intricacies of the Braess paradox. This volume invites readers to explore diverse perspectives and theoretical insights that are both practical and forward-thinking. This publication is an invaluable resource for graduate students and advanced researchers in the fields of optimization and discrete mathematics. It is particularly beneficial for those interested in their applications within data sciences. Academics across these disciplines will find the book's content relevant to their work, while practitioners seeking to apply these concepts in industry will appreciate its practical case studies. Whether you are a scholar or a professional, this book offers a wealth of knowledge that bridges theory with real-world applications.
Iterative Solution Of Large Sparse Systems Of Equations
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Author : Wolfgang Hackbusch
language : en
Publisher: Springer
Release Date : 2016-06-21
Iterative Solution Of Large Sparse Systems Of Equations written by Wolfgang Hackbusch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-21 with Mathematics categories.
In the second edition of this classic monograph, complete with four new chapters and updated references, readers will now have access to content describing and analysing classical and modern methods with emphasis on the algebraic structure of linear iteration, which is usually ignored in other literature. The necessary amount of work increases dramatically with the size of systems, so one has to search for algorithms that most efficiently and accurately solve systems of, e.g., several million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretization of partial differential equations. In this case, the matrices are sparse (i.e., they contain mostly zeroes) and well-suited to iterative algorithms. The first edition of this book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics. The second edition includes quite novel approaches.
The Isogeometric Boundary Element Method
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Author : Gernot Beer
language : en
Publisher: Springer Nature
Release Date : 2019-09-21
The Isogeometric Boundary Element Method written by Gernot Beer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-21 with Science categories.
This book discusses the introduction of isogeometric technology to the boundary element method (BEM) in order to establish an improved link between simulation and computer aided design (CAD) that does not require mesh generation. In the isogeometric BEM, non-uniform rational B-splines replace the Lagrange polynomials used in conventional BEM. This may seem a trivial exercise, but if implemented rigorously, it has profound implications for the programming, resulting in software that is extremely user friendly and efficient. The BEM is ideally suited for linking with CAD, as both rely on the definition of objects by boundary representation. The book shows how the isogeometric philosophy can be implemented and how its benefits can be maximised with a minimum of user effort. Using several examples, ranging from potential problems to elasticity, it demonstrates that the isogeometric approach results in a drastic reduction in the number of unknowns and an increase in the quality of the results. In some cases even exact solutions without refinement are possible. The book also presents a number of practical applications, demonstrating that the development is not only of academic interest. It then elegantly addresses heterogeneous and non-linear problems using isogeometric concepts, and tests them on several examples, including a severely non-linear problem in viscous flow. The book makes a significant contribution towards a seamless integration of CAD and simulation, which eliminates the need for tedious mesh generation and provides high-quality results with minimum user intervention and computing.
Euro Par 2018 Parallel Processing
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Author : Marco Aldinucci
language : en
Publisher: Springer
Release Date : 2018-08-20
Euro Par 2018 Parallel Processing written by Marco Aldinucci and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-20 with Computers categories.
This book constitutes the proceedings of the 24th International Conference on Parallel and Distributed Computing, Euro-Par 2018, held in Turin, Italy, in August 2018. The 57 full papers presented in this volume were carefully reviewed and selected from 194 submissions. They were organized in topical sections named: support tools and environments; performance and power modeling, prediction and evaluation; scheduling and load balancing; high performance architecutres and compilers; parallel and distributed data management and analytics; cluster and cloud computing; distributed systems and algorithms; parallel and distributed programming, interfaces, and languages; multicore and manycore methods and tools; theory and algorithms for parallel computation and networking; parallel numerical methods and applications; and accelerator computing for advanced applications.
Efficient Numerical Methods For Non Local Operators
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Author : Steffen Börm
language : en
Publisher: European Mathematical Society
Release Date : 2010
Efficient Numerical Methods For Non Local Operators written by Steffen Börm and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
Hierarchical matrices present an efficient way of treating dense matrices that arise in the context of integral equations, elliptic partial differential equations, and control theory. While a dense $n\times n$ matrix in standard representation requires $n^2$ units of storage, a hierarchical matrix can approximate the matrix in a compact representation requiring only $O(n k \log n)$ units of storage, where $k$ is a parameter controlling the accuracy. Hierarchical matrices have been successfully applied to approximate matrices arising in the context of boundary integral methods, to construct preconditioners for partial differential equations, to evaluate matrix functions, and to solve matrix equations used in control theory. $\mathcal{H}^2$-matrices offer a refinement of hierarchical matrices: Using a multilevel representation of submatrices, the efficiency can be significantly improved, particularly for large problems. This book gives an introduction to the basic concepts and presents a general framework that can be used to analyze the complexity and accuracy of $\mathcal{H}^2$-matrix techniques. Starting from basic ideas of numerical linear algebra and numerical analysis, the theory is developed in a straightforward and systematic way, accessible to advanced students and researchers in numerical mathematics and scientific computing. Special techniques are required only in isolated sections, e.g., for certain classes of model problems.
Siam Journal On Matrix Analysis And Applications
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Author :
language : en
Publisher:
Release Date : 1997
Siam Journal On Matrix Analysis And Applications written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.