Direct Methods for Sparse Matrices

DOWNLOAD NOW »

Author: I. S. Duff,A. M. Erisman,J. K. Reid

Publisher: Oxford University Press

ISBN: 0192507508

Category: Mathematics

Page: 416

View: 7336

The subject of sparse matrices has its root in such diverse fields as management science, power systems analysis, surveying, circuit theory, and structural analysis. Efficient use of sparsity is a key to solving large problems in many fields. This second edition is a complete rewrite of the first edition published 30 years ago. Much has changed since that time. Problems have grown greatly in size and complexity; nearly all examples in the first edition were of order less than 5,000 in the first edition, and are often more than a million in the second edition. Computer architectures are now much more complex, requiring new ways of adapting algorithms to parallel environments with memory hierarchies. Because the area is such an important one to all of computational science and engineering, a huge amount of research has been done in the last 30 years, some of it by the authors themselves. This new research is integrated into the text with a clear explanation of the underlying mathematics and algorithms. New research that is described includes new techniques for scaling and error control, new orderings, new combinatorial techniques for partitioning both symmetric and unsymmetric problems, and a detailed description of the multifrontal approach to solving systems that was pioneered by the research of the authors and colleagues. This includes a discussion of techniques for exploiting parallel architectures and new work for indefinite and unsymmetric systems.

Computer Algebra in Scientific Computing

18th International Workshop, CASC 2016, Bucharest, Romania, September 19-23, 2016, Proceedings

DOWNLOAD NOW »

Author: Vladimir P. Gerdt,Wolfram Koepf,Werner M. Seiler,Evgenii V. Vorozhtsov

Publisher: Springer

ISBN: 3319456415

Category: Computers

Page: 513

View: 533

This book constitutes the proceedings of the 18th International Workshop on Computer Algebra in Scientific Computing, CASC 2016, held in Bucharest, Romania, in September 2016. The 32 papers presented in this volume were carefully reviewed and selected from 39 submissions. They deal with cutting-edge research in all major disciplines of Computer Algebra.

Transactions on Large-Scale Data- and Knowledge-Centered Systems VII

DOWNLOAD NOW »

Author: Abdelkader Hameurlain,Josef Küng,Roland Wagner

Publisher: Springer

ISBN: 3642353320

Category: Computers

Page: 171

View: 707

The LNCS journal Transactions on Large-Scale Data- and Knowledge-Centered Systems focuses on data management, knowledge discovery, and knowledge processing, which are core and hot topics in computer science. Since the 1990s, the Internet has become the main driving force behind application development in all domains. An increase in the demand for resource sharing across different sites connected through networks has led to an evolution of data- and knowledge-management systems from centralized systems to decentralized systems enabling large-scale distributed applications providing high scalability. Current decentralized systems still focus on data and knowledge as their main resource. Feasibility of these systems relies basically on P2P (peer-to-peer) techniques and the support of agent systems with scaling and decentralized control. Synergy between grids, P2P systems, and agent technologies is the key to data- and knowledge-centered systems in large-scale environments. This, the seventh issue of Transactions on Large-Scale Data- and Knowledge-Centered Systems, contains five revised selected regular papers on the following topics: data management, data streams, service-oriented computing, abstract algebraic frameworks, RDF and ontologies, and conceptual model frameworks.

Computational Methods for General Sparse Matrices

DOWNLOAD NOW »

Author: Zahari Zlatev

Publisher: Springer Science & Business Media

ISBN: 940171116X

Category: Computers

Page: 328

View: 4107

'Et moi ... - si j'avait su comment en revenir, One service mathematics has rendered the je n 'y serais point aile.' human race. It has put common sense back where it belongs, on the topmost shelf next Jules Verne to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell 0. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'elre of this series.

Direct Methods for Sparse Linear Systems

DOWNLOAD NOW »

Author: Timothy A. Davis

Publisher: SIAM

ISBN: 0898716136

Category: Computers

Page: 217

View: 5601

The sparse backslash book. Everything you wanted to know but never dared to ask about modern direct linear solvers. Chen Greif, Assistant Professor, Department of Computer Science, University of British Columbia.Overall, the book is magnificent. It fills a long-felt need for an accessible textbook on modern sparse direct methods. Its choice of scope is excellent John Gilbert, Professor, Department of Computer Science, University of California, Santa Barbara.Computational scientists often encounter problems requiring the solution of sparse systems of linear equations. Attacking these problems efficiently requires an in-depth knowledge of the underlying theory, algorithms, and data structures found in sparse matrix software libraries. Here, Davis presents the fundamentals of sparse matrix algorithms to provide the requisite background. The book includes CSparse, a concise downloadable sparse matrix package that illustrates the algorithms and theorems presented in the book and equips readers with the tools necessary to understand larger and more complex software packages.With a strong emphasis on MATLAB and the C programming language, Direct Methods for Sparse Linear Systems equips readers with the working knowledge required to use sparse solver packages and write code to interface applications to those packages. The book also explains how MATLAB performs its sparse matrix computations.Audience This invaluable book is essential to computational scientists and software developers who want to understand the theory and algorithms behind modern techniques used to solve large sparse linear systems. The book also serves as an excellent practical resource for students with an interest in combinatorial scientific computing.Preface; Chapter 1: Introduction; Chapter 2: Basic algorithms; Chapter 3: Solving triangular systems; Chapter 4: Cholesky factorization; Chapter 5: Orthogonal methods; Chapter 6: LU factorization; Chapter 7: Fill-reducing orderings; Chapter 8: Solving sparse linear systems; Chapter 9: CSparse; Chapter 10: Sparse matrices in MATLAB; Appendix: Basics of the C programming language; Bibliography; Index.

Numerical Methods in Matrix Computations

DOWNLOAD NOW »

Author: Åke Björck

Publisher: Springer

ISBN: 3319050893

Category: Mathematics

Page: 800

View: 1297

Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given. Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work.

Computational Methods for Large Sparse Power Systems Analysis

An Object Oriented Approach

DOWNLOAD NOW »

Author: S. A. Soman,S. A. Khaparde,Shubha Pandit

Publisher: Springer Science & Business Media

ISBN: 9780792375913

Category: Computers

Page: 333

View: 4901

Computational methods in Power Systems require significant inputs from diverse disciplines, such as data base structures, numerical analysis etc. Strategic decisions in sparsity exploitation and algorithm design influence large-scale simulation and high-speed computations. Selection of programming paradigm shapes the design, its modularity and reusability. This has a far reaching effect on software maintenance. Computational Methods for Large Sparse Power Systems Analysis: An Object Oriented Approach provides a unified object oriented (OO) treatment for power system analysis. Sparsity exploitation techniques in OO paradigm are emphasized to facilitate large scale and fast computing. Specific applications like large-scale load flow, short circuit analysis, state estimation and optimal power flow are discussed within this framework. A chapter on modeling and computational issues in power system dynamics is also included. Motivational examples and illustrations are included throughout the book. A library of C++ classes provided along with this book has classes for transmission lines, transformers, substation etc. A CD-ROM with C++ programs is also included. It contains load flow, short circuit analysis and network topology processor applications. Power system data is provided and systems up to 150 buses can be studied. Other Special Features: This book is the first of its kind, covering power system applications designed with an OO perspective. Chapters on object orientation for modeling of power system computations, data structure, large sparse linear system solver, sparse QR decomposition in an OO framework are special features of this book.

High-Performance Scientific Computing

Algorithms and Applications

DOWNLOAD NOW »

Author: Michael W. Berry,Kyle A. Gallivan,Efstratios Gallopoulos,Ananth Grama,Bernard Philippe,Yousef Saad,Faisal Saied

Publisher: Springer Science & Business Media

ISBN: 1447124367

Category: Computers

Page: 350

View: 7056

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.

Angewandte Mathematik: Body and Soul

Band 2: Integrale und Geometrie in IRn

DOWNLOAD NOW »

Author: Kenneth Eriksson,Donald Estep,Claes Johnson

Publisher: Springer-Verlag

ISBN: 3540269509

Category: Mathematics

Page: 362

View: 7952

"Angewandte Mathematik: Body & Soul" ist ein neuer Grundkurs in der Mathematikausbildung für Studienanfänger in den Naturwissenschaften, der Technik, und der Mathematik, der an der Chalmers Tekniska Högskola in Göteborg entwickelt wurde. Er besteht aus drei Bänden sowie Computer-Software. Das Projekt ist begründet in der Computerrevolution, die ihrerseits völlig neue Möglichkeiten des wissenschaftlichen Rechnens in der Mathematik, den Naturwissenschaften und im Ingenieurwesen eröffnet hat. Es besteht aus einer Synthese der mathematischen Analysis (Soul) mit der numerischen Berechnung (Body) sowie den Anwendungen. Die Bände I-III geben eine moderne Version der Analysis und der linearen Algebra wieder, einschließlich konstruktiver numerischer Techniken und Anwendungen, zugeschnitten auf Anfängerprogramme im Maschinenbau und den Naturwissenschaften. Weitere Bände behandeln Themen wie z.B. dynamische Systeme, Strömungsdynamik, Festkörpermechanik und Elektromagnetismus. Dieser Band entwickelt das Riemann-Integral, um eine Funktion zu einer gegebenen Ableitung zu bestimmen. Darauf aufbauend werden Differentialgleichungen und Anfangswertprobleme mit einer Vielzahl anschaulicher Anwendungen behandelt. Die lineare Algebra wird auf n-dimensionale Räume verallgemeinert, wobei wiederum dem praktischen Umgang und numerischen Lösungstechniken besonderer Platz eingeräumt wird. Die Autoren sind führende Experten im Gebiet des wissenschaftlichen Rechnens und haben schon mehrere erfolgreiche Bücher geschrieben. "[......] Oh, by the way, I suggest immediate purchase of all three volumes!" The Mathematical Association of America Online, 7.7.04

Large-Scale Scientific Computing

Third International Conference, LSSC 2001, Sozopol, Bulgaria, June 6-10, 2001. Revised Papers

DOWNLOAD NOW »

Author: Svetozar Margenov,LSSC,Jerzy Wasniewski

Publisher: Springer Science & Business Media

ISBN: 3540430431

Category: Computers

Page: 498

View: 2673

Thepurposeoftheconferencewastobringtogetherscientistsworkingwith largecomputationalproblemsinindustry,andspecialistsinthe?eldofnume- calanalysis‘methodsande?cientexploitationofmodernhigh-speedcomputers. Someclassesofmethodsappearagainandagaininthenumericaltreatmentof problemsfromdi?erent?eldsofscienceandengineering. Theaimofthisconf- encewastoselectsomeofthesenumericalmethodsandplanfurtherexperiments onseveraltypesofparallelcomputers. Thekeylecturesreviewedthemostimp- tantnumericalalgorithmsandscienti?capplicationsonparallelcomputers. The invited speakers included university and practical engineers from industry, as wellasappliedmathematicians,numericalanalysts,andcomputerexperts.

Data-Driven Modeling & Scientific Computation

Methods for Complex Systems & Big Data

DOWNLOAD NOW »

Author: J. Nathan Kutz

Publisher: OUP Oxford

ISBN: 019163588X

Category: Language Arts & Disciplines

Page: 608

View: 9614

The burgeoning field of data analysis is expanding at an incredible pace due to the proliferation of data collection in almost every area of science. The enormous data sets now routinely encountered in the sciences provide an incentive to develop mathematical techniques and computational algorithms that help synthesize, interpret and give meaning to the data in the context of its scientific setting. A specific aim of this book is to integrate standard scientific computing methods with data analysis. By doing so, it brings together, in a self-consistent fashion, the key ideas from: · statistics, · time-frequency analysis, and · low-dimensional reductions The blend of these ideas provides meaningful insight into the data sets one is faced with in every scientific subject today, including those generated from complex dynamical systems. This is a particularly exciting field and much of the final part of the book is driven by intuitive examples from it, showing how the three areas can be used in combination to give critical insight into the fundamental workings of various problems. Data-Driven Modeling and Scientific Computation is a survey of practical numerical solution techniques for ordinary and partial differential equations as well as algorithms for data manipulation and analysis. Emphasis is on the implementation of numerical schemes to practical problems in the engineering, biological and physical sciences. An accessible introductory-to-advanced text, this book fully integrates MATLAB and its versatile and high-level programming functionality, while bringing together computational and data skills for both undergraduate and graduate students in scientific computing.

Wissenschaftliches Rechnen mit MATLAB

DOWNLOAD NOW »

Author: Alfio Quarteroni,Fausto Saleri

Publisher: Springer-Verlag

ISBN: 3540293078

Category: Mathematics

Page: 269

View: 1090

Aus den Rezensionen der englischen Auflage: Dieses Lehrbuch ist eine Einführung in das Wissenschaftliche Rechnen und diskutiert Algorithmen und deren mathematischen Hintergrund. Angesprochen werden im Detail nichtlineare Gleichungen, Approximationsverfahren, numerische Integration und Differentiation, numerische Lineare Algebra, gewöhnliche Differentialgleichungen und Randwertprobleme. Zu den einzelnen Themen werden viele Beispiele und Übungsaufgaben sowie deren Lösung präsentiert, die durchweg in MATLAB formuliert sind. Der Leser findet daher nicht nur die graue Theorie sondern auch deren Umsetzung in numerischen, in MATLAB formulierten Code. MATLAB select 2003, Issue 2, p. 50. [Die Autoren] haben ein ausgezeichnetes Werk vorgelegt, das MATLAB vorstellt und eine sehr nützliche Sammlung von MATLAB Funktionen für die Lösung fortgeschrittener mathematischer und naturwissenschaftlicher Probleme bietet. [...] Die Präsentation des Stoffs ist durchgängig gut und leicht verständlich und beinhaltet Lösungen für die Übungen am Ende jedes Kapitels. Als exzellenter Neuzugang für Universitätsbibliotheken- und Buchhandlungen wird dieses Buch sowohl beim Selbststudium als auch als Ergänzung zu anderen MATLAB-basierten Büchern von großem Nutzen sein. Alles in allem: Sehr empfehlenswert. Für Studenten im Erstsemester wie für Experten gleichermassen. S.T. Karris, University of California, Berkeley, Choice 2003.

Mathematical Physics and Stochastic Analysis

Essays in Honour of Ludwig Streit

DOWNLOAD NOW »

Author: Sergio Albeverio

Publisher: World Scientific

ISBN: 9789810244408

Category: Science

Page: 438

View: 4991

In October 1998 a conference was held in Lisbon to celebrate Ludwig Streit's 60th birthday. This book collects some of the papers presented at the conference as well as other essays contributed by the many friends and collaborators who wanted to honor Ludwig Streit's scientific career and personality.The contributions cover many aspects of contemporary mathematical physics. Of particular importance are new results on infinite-dimensional stochastic analysis and its applications to a wide range of physical domains.List of Contributors: S Albeverio, T Hida, L Accardi, I Ya Aref'eva, I V Volovich; A Daletskii, Y Kondratiev, W Karwowski, N Asai, I Kubo, H-H Kuo, J Beckers, Ph Blanchard, G F Dell'Antonio, D Gandolfo, M Sirugue-Collin, A Bohm, H Kaldass, D Boll‚, G Jongen, G M Shim, J Bornales, C C Bernido, M V Carpio-Bernido, G Burdet, Ph Combe, H Nencka, P Cartier, C DeWitt-Morette, H Ezawa, K Nakamura, K Watanabe, Y Yamanaka, R Figari, F Gesztesy, H Holden, R Gielerak, G A Goldin, Z Haba, M-O Hongler, Y Hu, B Oksendal, A Sulem, J R Klauder, C B Lang, V I Man'ko, H Ouerdiane, J Potthoff, E Smajlovic, M R”ckner, E Scacciatelli, J L Silva, J Stochel, F H Szafraniec, L V zquez, D N Kozakevich, S Jim‚nez, V R Vieira, P D Sacramento, R Vilela Mendes, D Voln?, P Samek.

Modelling and computation for applications in mathematics, science, and engineering

DOWNLOAD NOW »

Author: Joseph W. Jerome

Publisher: Oxford University Press, USA

ISBN: N.A

Category: Computers

Page: 215

View: 9590

This book discusses many of the connections between cutting edge applications and advanced numerical and algorithmic techniques. Topics include models for long-range molecular forces; biological and chemical contamination, including hierarchical problem-solving ideas from computer science; discrete mathematics, including connections to the buckyball structure of carbon 60; dimension-reduction techniques in incompressible fluid mechanics; aspects of charge transport, bridging compressible fluids (gas dynamics) and semiconductors; the approximation problem in control theory; questions related to weighted approximation by polynomials in the complex plane; and high friction limits of hydrodynamic models.