Scientific Computing Validated Numerics Interval Methods

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Scientific Computing, Validated Numerics, Interval Methods

Author : Walter Krämer
Publisher : Springer Science & Business Media
ISBN 13 : 1475764847
Total Pages : 385 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Scientific Computing, Validated Numerics, Interval Methods by : Walter Krämer

Download or read book Scientific Computing, Validated Numerics, Interval Methods written by Walter Krämer and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scan 2000, the GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics and Interval 2000, the International Conference on Interval Methods in Science and Engineering were jointly held in Karlsruhe, September 19-22, 2000. The joint conference continued the series of 7 previous Scan-symposia under the joint sponsorship of GAMM and IMACS. These conferences have traditionally covered the numerical and algorithmic aspects of scientific computing, with a strong emphasis on validation and verification of computed results as well as on arithmetic, programming, and algorithmic tools for this purpose. The conference further continued the series of 4 former Interval conferences focusing on interval methods and their application in science and engineering. The objectives are to propagate current applications and research as well as to promote a greater understanding and increased awareness of the subject matters. The symposium was held in Karlsruhe the European cradle of interval arithmetic and self-validating numerics and attracted 193 researchers from 33 countries. 12 invited and 153 contributed talks were given. But not only the quantity was overwhelming we were deeply impressed by the emerging maturity of our discipline. There were many talks discussing a wide variety of serious applications stretching all parts of mathematical modelling. New efficient, publicly available or even commercial tools were proposed or presented, and also foundations of the theory of intervals and reliable computations were considerably strengthened.

Scientific Computing, Computer Arithmetic, and Validated Numerics

Author : Marco Nehmeier
Publisher : Springer
ISBN 13 : 3319317695
Total Pages : 291 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Scientific Computing, Computer Arithmetic, and Validated Numerics by : Marco Nehmeier

Download or read book Scientific Computing, Computer Arithmetic, and Validated Numerics written by Marco Nehmeier and published by Springer. This book was released on 2016-04-08 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed post proceedings of the 16th International Symposium, SCAN 2014, held in Würzburg, Germany, in September 2014. The 22 full papers presented were carefully reviewed and selected from 60 submissions. The main concerns of research addressed by SCAN conferences are validation, verification or reliable assertions of numerical computations. Interval arithmetic and other treatments of uncertainty are developed as appropriate tools.

Validated Numerics

Author : Warwick Tucker
Publisher : Princeton University Press
ISBN 13 : 069124765X
Total Pages : 152 pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis Validated Numerics by : Warwick Tucker

Download or read book Validated Numerics written by Warwick Tucker and published by Princeton University Press. This book was released on 2023-06-06 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, self-contained primer on validated numerics This textbook provides a comprehensive introduction to the theory and practice of validated numerics, an emerging new field that combines the strengths of scientific computing and pure mathematics. In numerous fields ranging from pharmaceutics and engineering to weather prediction and robotics, fast and precise computations are essential. Based on the theory of set-valued analysis, a new suite of numerical methods is developed, producing efficient and reliable solvers for numerous problems in nonlinear analysis. Validated numerics yields rigorous computations that can find all possible solutions to a problem while taking into account all possible sources of error—fast, and with guaranteed accuracy. Validated Numerics offers a self-contained primer on the subject, guiding readers from the basics to more advanced concepts and techniques. This book is an essential resource for those entering this fast-developing field, and it is also the ideal textbook for graduate students and advanced undergraduates needing an accessible introduction to the subject. Validated Numerics features many examples, exercises, and computer labs using MATLAB/C++, as well as detailed appendixes and an extensive bibliography for further reading. Provides a comprehensive, self-contained introduction to validated numerics Requires no advanced mathematics or programming skills Features many examples, exercises, and computer labs Includes code snippets that illustrate implementation Suitable as a textbook for graduate students and advanced undergraduates

Scientific Computing and Validated Numerics

Author : G. Alefeld
Publisher : De Gruyter Akademie Forschung
ISBN 13 :
Total Pages : 348 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Scientific Computing and Validated Numerics by : G. Alefeld

Download or read book Scientific Computing and Validated Numerics written by G. Alefeld and published by De Gruyter Akademie Forschung. This book was released on 1996 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics SCAN is held biannually, the fourth conference took place in Wuppertal 1995. This volume contains contributions from outstanding research specialists based on their presentations at SCAN-95. It covers all aspects of scientific computing with validation, starting with the latest developments in the design of floating point units together with algorithms for floating point operations and elementary function evaluations with maximum accuracy. The book continues by treating scientific computing methods for many areas of applied mathematics such as numerical linear algebra, nonlinear equations, global optimization, ordinary and partial differential equations and dynamical systems. Some computer science aspects like complexity are also considered as are examples where validation methods have successfully be used in applications from the engineering sciences.

Large-Scale Scientific Computing

Author : Ivan Lirkov
Publisher : Springer
ISBN 13 : 3540788271
Total Pages : 754 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Large-Scale Scientific Computing by : Ivan Lirkov

Download or read book Large-Scale Scientific Computing written by Ivan Lirkov and published by Springer. This book was released on 2009-03-26 with total page 754 pages. Available in PDF, EPUB and Kindle. Book excerpt: Coverage in this proceedings volume includes robust multilevel and hierarchical preconditioning methods, applications for large scale computations and optimization of coupled engineering problems, and applications of metaheuristics to large-scale problems.

Numerical Methods and Applications

Author : Lirkov Ivan Dimov
Publisher : Springer
ISBN 13 : 3642184669
Total Pages : 524 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Numerical Methods and Applications by : Lirkov Ivan Dimov

Download or read book Numerical Methods and Applications written by Lirkov Ivan Dimov and published by Springer. This book was released on 2011-01-27 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 7th International Conference on Numerical Methods and Applications, NMA 2010, held in Borovets, Bulgaria, in August 2010. The 60 revised full papers presented together with 3 invited papers were carefully reviewed and selected from numerous submissions for inclusion in this book. The papers are organized in topical sections on Monte Carlo and quasi-Monte Carlo methods, environmental modeling, grid computing and applications, metaheuristics for optimization problems, and modeling and simulation of electrochemical processes.

Granular, Fuzzy, and Soft Computing

Author : Tsau-Young Lin
Publisher : Springer Nature
ISBN 13 : 1071626280
Total Pages : 936 pages
Book Rating : 4.0/5 (716 download)

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Book Synopsis Granular, Fuzzy, and Soft Computing by : Tsau-Young Lin

Download or read book Granular, Fuzzy, and Soft Computing written by Tsau-Young Lin and published by Springer Nature. This book was released on 2023-03-29 with total page 936 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of the Encyclopedia of Complexity and Systems Science (ECSS, 2009) presented a comprehensive overview of granular computing (GrC) broadly divided into several categories: Granular computing from rough set theory, Granular Computing in Database Theory, Granular Computing in Social Networks, Granular Computing and Fuzzy Set Theory, Grid/Cloud Computing, as well as general issues in granular computing. In 2011, the formal theory of GrC was established, providing an adequate infrastructure to support revolutionary new approaches to computer/data science, including the challenges presented by so-called big data. For this volume of ECSS, Second Edition, many entries have been updated to capture these new developments, together with new chapters on such topics as data clustering, outliers in data mining, qualitative fuzzy sets, and information flow analysis for security applications. Granulations can be seen as a natural and ancient methodology deeply rooted in the human mind. Many daily "things" are routinely granulated into sub "things": The topography of earth is granulated into hills, plateaus, etc., space and time are granulated into infinitesimal granules, and a circle is granulated into polygons of infinitesimal sides. Such granules led to the invention of calculus, topology and non-standard analysis. Formalization of general granulation was difficult but, as shown in this volume, great progress has been made in combing discrete and continuous mathematics under one roof for a broad range of applications in data science.

SCAN'2000

Author : Stefan Dietrich
Publisher :
ISBN 13 :
Total Pages : 199 pages
Book Rating : 4.:/5 (87 download)

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Book Synopsis SCAN'2000 by : Stefan Dietrich

Download or read book SCAN'2000 written by Stefan Dietrich and published by . This book was released on 2000 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Numerical Methods and Applications

Author : Todor Boyanov
Publisher : Springer
ISBN 13 : 3540709428
Total Pages : 742 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Numerical Methods and Applications by : Todor Boyanov

Download or read book Numerical Methods and Applications written by Todor Boyanov and published by Springer. This book was released on 2007-05-15 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-proceedings of NMA 2006 held in Borovets, Bulgaria. Coverage in the 84 revised full papers includes numerical methods for hyperbolic problems, robust preconditioning solution methods, metaheuristics for optimization problems, uncertain/control systems and reliable numerics, interpolation and quadrature processes, and large-scale computations in environmental modeling.

Numerical Validation in Current Hardware Architectures

Author : Annie A.M. Cuyt
Publisher : Springer Science & Business Media
ISBN 13 : 3642015905
Total Pages : 272 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Numerical Validation in Current Hardware Architectures by : Annie A.M. Cuyt

Download or read book Numerical Validation in Current Hardware Architectures written by Annie A.M. Cuyt and published by Springer Science & Business Media. This book was released on 2009-04-24 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: The major emphasis of the Dagstuhl Seminar on “Numerical Validation in C- rent Hardware Architectures” lay on numerical validation in current hardware architecturesand softwareenvironments. The generalidea wasto bring together experts who are concerned with computer arithmetic in systems with actual processor architectures and scientists who develop, use, and need techniques from veri?ed computation in their applications. Topics of the seminar therefore included: – The ongoing revision of the IEEE 754/854 standard for ?oating-point ari- metic – Feasible ways to implement multiple precision (multiword) arithmetic and to compute the actual precision at run-time according to the needs of input data – The achievement of a similar behavior of ?xed-point, ?oating-point and - terval arithmetic across language compliant implementations – The design of robust and e?cient numerical programsportable from diverse computers to those that adhere to the IEEE standard – The development and propagation of validated special-purpose software in di?erent application areas – Error analysis in several contexts – Certi?cation of numerical programs, veri?cation and validation assessment Computer arithmetic plays an important role at the hardware and software level, when microprocessors, embedded systems, or grids are designed. The re- ability of numerical softwarestrongly depends on the compliance with the cor- sponding ?oating-point norms. Standard CISC processors follow the 1985 IEEE norm 754, which is currently under revision, but the new highly performing CELL processor is not fully IEEE compliant.

Numerical Software with Result Verification

Author : René Alt
Publisher : Springer
ISBN 13 : 3540247386
Total Pages : 324 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Numerical Software with Result Verification by : René Alt

Download or read book Numerical Software with Result Verification written by René Alt and published by Springer. This book was released on 2004-02-12 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reliable computing techniques are essential if the validity of the output of a - merical algorithm is to be guaranteed to be correct. Our society relies more and more on computer systems. Usually, our systems appear to work successfully, but there are sometimes serious, and often minor, errors. Validated computing is one essential technology to achieve increased software reliability. Formal - gor in the de?nition of data types, the computer arithmetic, in algorithm design, and in program execution allows us to guarantee that the stated problem has (or does not have) a solution in an enclosing interval we compute. If the enclosure is narrow, we are certain that the result can be used. Otherwise, we have a clear warning that the uncertainty of input values might be large and the algorithm and the model have to be improved. The use of interval data types and al- rithms with controlled rounding and result veri?cation capture uncertainty in modeling and problem formulation, in model parameter estimation, in algorithm truncation, in operation round-o?, and in model interpretation. The techniques of validated computing have proven their merits in many scienti?c and engineering applications. They are based on solid and interesting theoretical studies in mathematics and computer science. Contributions from ?elds including real, complex and functional analysis, semigroups, probability, statistics,fuzzyintervalanalysis,fuzzylogic,automaticdi?erentiation,computer hardware, operating systems, compiler construction, programming languages, object-oriented modeling, parallel processing, and software engineering are all essential.

Parallel Processing and Applied Mathematics, Part II

Author : Roman Wyrzykowski
Publisher : Springer
ISBN 13 : 3642144039
Total Pages : 620 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Parallel Processing and Applied Mathematics, Part II by : Roman Wyrzykowski

Download or read book Parallel Processing and Applied Mathematics, Part II written by Roman Wyrzykowski and published by Springer. This book was released on 2010-07-07 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Handbook of Granular Computing

Author : Witold Pedrycz
Publisher : John Wiley & Sons
ISBN 13 : 0470724153
Total Pages : 1148 pages
Book Rating : 4.4/5 (77 download)

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Book Synopsis Handbook of Granular Computing by : Witold Pedrycz

Download or read book Handbook of Granular Computing written by Witold Pedrycz and published by John Wiley & Sons. This book was released on 2008-07-31 with total page 1148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the notion is a relatively recent one, the notions and principles of Granular Computing (GrC) have appeared in a different guise in many related fields including granularity in Artificial Intelligence, interval computing, cluster analysis, quotient space theory and many others. Recent years have witnessed a renewed and expanding interest in the topic as it begins to play a key role in bioinformatics, e-commerce, machine learning, security, data mining and wireless mobile computing when it comes to the issues of effectiveness, robustness and uncertainty. The Handbook of Granular Computing offers a comprehensive reference source for the granular computing community, edited by and with contributions from leading experts in the field. Includes chapters covering the foundations of granular computing, interval analysis and fuzzy set theory; hybrid methods and models of granular computing; and applications and case studies. Divided into 5 sections: Preliminaries, Fundamentals, Methodology and Algorithms, Development of Hybrid Models and Applications and Case Studies. Presents the flow of ideas in a systematic, well-organized manner, starting with the concepts and motivation and proceeding to detailed design that materializes in specific algorithms, applications and case studies. Provides the reader with a self-contained reference that includes all pre-requisite knowledge, augmented with step-by-step explanations of more advanced concepts. The Handbook of Granular Computing represents a significant and valuable contribution to the literature and will appeal to a broad audience including researchers, students and practitioners in the fields of Computational Intelligence, pattern recognition, fuzzy sets and neural networks, system modelling, operations research and bioinformatics.

Computer Arithmetic and Self-Validating Numerical Methods

Author : Christian Ullrich
Publisher : Academic Press
ISBN 13 : 1483267814
Total Pages : 316 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Computer Arithmetic and Self-Validating Numerical Methods by : Christian Ullrich

Download or read book Computer Arithmetic and Self-Validating Numerical Methods written by Christian Ullrich and published by Academic Press. This book was released on 2014-05-10 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Notes and Reports in Mathematics in Science and Engineering, Volume VII: Computer Arithmetic and Self-Validating Numerical Methods compiles papers presented at the first international conference on “Computer Arithmetic and Self-Validating Numerical Methods, held in Basel from October 2 to 6, 1989. This book begins by providing a tutorial introduction to computer arithmetic with operations of maximum accuracy, differentiation arithmetic and enclosure methods, and programming languages for self-validating numerical methods. The rest of the chapters discuss the determination of guaranteed bounds for eigenvalues by variational methods and guaranteed inclusion of solutions of differential equations. An appendix covering the IMACS-GAMM resolution on computer arithmetic is provided at the end of this publication. This volume is recommended for researchers and professionals working on computer arithmetic and self-validating numerical methods.

Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures

Author : George Deodatis
Publisher : CRC Press
ISBN 13 : 1315884887
Total Pages : 1112 pages
Book Rating : 4.3/5 (158 download)

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Book Synopsis Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures by : George Deodatis

Download or read book Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures written by George Deodatis and published by CRC Press. This book was released on 2014-02-10 with total page 1112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures contains the plenary lectures and papers presented at the 11th International Conference on STRUCTURAL SAFETY AND RELIABILITY (ICOSSAR2013, New York, NY, USA, 16-20 June 2013), and covers major aspects of safety, reliability, risk and life-cycle performance of str

Interval Methods for Solving Nonlinear Constraint Satisfaction, Optimization and Similar Problems

Author : Bartłomiej Jacek Kubica
Publisher : Springer
ISBN 13 : 3030137953
Total Pages : 156 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Interval Methods for Solving Nonlinear Constraint Satisfaction, Optimization and Similar Problems by : Bartłomiej Jacek Kubica

Download or read book Interval Methods for Solving Nonlinear Constraint Satisfaction, Optimization and Similar Problems written by Bartłomiej Jacek Kubica and published by Springer. This book was released on 2019-03-08 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights recent research on interval methods for solving nonlinear constraint satisfaction, optimization and similar problems. Further, it presents a comprehensive survey of applications in various branches of robotics, artificial intelligence systems, economics, control theory, dynamical systems theory, and others. Three appendices, on the notation, representation of numbers used as intervals’ endpoints, and sample implementations of the interval data type in several programming languages, round out the coverage.

Efficient Algorithms for Verified Scientific Computing

Author : Hong Diep Nguyen (informaticien).)
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (8 download)

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Book Synopsis Efficient Algorithms for Verified Scientific Computing by : Hong Diep Nguyen (informaticien).)

Download or read book Efficient Algorithms for Verified Scientific Computing written by Hong Diep Nguyen (informaticien).) and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interval arithmetic is a means to compute verified results. However, a naive use of interval arithmetic does not provide accurate enclosures of the exact results. Moreover, interval arithmetic computations can be time-consuming. We propose several accurate algorithms and efficient implementations in verified linear algebra using interval arithmetic. Two fundamental problems are addressed, namely the multiplication of interval matrices and the verification of a floating-point solution of a linear system. For the first problem, we propose two algorithms which offer new tradeoffs between speed and accuracy. For the second problem, which is the verification of the solution of a linear system, our main contributions are twofold. First, we introduce a relaxation technique, which reduces drastically the execution time of the algorithm. Second, we propose to use extended precision for few, well-chosen parts of the computations, to gain accuracy without losing much in term of execution time.