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Author: Ulrich Kulisch Publisher: Springer Science & Business Media ISBN: 3709162823 Category : Mathematics Languages : en Pages : 344
Book Description
Enclosure methods and their applications have been developed to a high standard during the last decades. These methods guarantee the validity of the computed results. This means they are of the same standard as the rest of mathematics. The book deals with a wide variety of aspects of enclosure methods. All contributions follow the common goal to push the limits of enclosure methods forward. Topics that are treated include basic questions of arithmetic, proving conjectures, bounds for Krylow type linear system solvers, bounds for eigenvalues, the wrapping effect, algorithmic differencing, differential equations, finite element methods, application in robotics, and nonsmooth global optimization.
Author: Ulrich Kulisch Publisher: Springer Science & Business Media ISBN: 3709162823 Category : Mathematics Languages : en Pages : 344
Book Description
Enclosure methods and their applications have been developed to a high standard during the last decades. These methods guarantee the validity of the computed results. This means they are of the same standard as the rest of mathematics. The book deals with a wide variety of aspects of enclosure methods. All contributions follow the common goal to push the limits of enclosure methods forward. Topics that are treated include basic questions of arithmetic, proving conjectures, bounds for Krylow type linear system solvers, bounds for eigenvalues, the wrapping effect, algorithmic differencing, differential equations, finite element methods, application in robotics, and nonsmooth global optimization.
Author: Lidiya Atanassova Publisher: North Holland ISBN: Category : Computer algorithms Languages : en Pages : 524
Book Description
Scientists concerned with the interaction between computer arithmetic, programming languages and scientific computing will be particularly interested in this book. It focuses on papers presented at the conference and highlights the increasing impact of SCAN-91 in this area. The volume contains original research and expository articles on the field of interaction between computer arithmetic and its realization in programming languages and the construction and investigation of numerical algorithms for computing guaranteed error-bounds for the solution of various problems in applied mathematics and engineering. Main subjects are: software tools for enclosure algorithms and inclusion methods with the help of interval arithmetic, in particular for the numerical solution of differential equations.
Author: Christian Ullrich Publisher: Academic Press ISBN: 1483267814 Category : Computers Languages : en Pages : 316
Book Description
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.
Author: Ulrich Kulisch Publisher: Walter de Gruyter ISBN: 3110301792 Category : Mathematics Languages : en Pages : 456
Book Description
This is the revised and extended second edition of the successful basic book on computer arithmetic. It is consistent with the newest recent standard developments in the field. The book shows how the arithmetic and mathematical capability of the digital computer can be enhanced in a quite natural way. The work is motivated by the desire and the need to improve the accuracy of numerical computing and to control the quality of the computed results (validity). The accuracy requirements for the elementary floating-point operations are extended to the customary product spaces of computations including interval spaces. The mathematical properties of these models are extracted into an axiomatic approach which leads to a general theory of computer arithmetic. Detailed methods and circuits for the implementation of this advanced computer arithmetic on digital computers are developed in part two of the book. Part three then illustrates by a number of sample applications how this extended computer arithmetic can be used to compute highly accurate and mathematically verified results. The book can be used as a high-level undergraduate textbook but also as reference work for research in computer arithmetic and applied mathematics.
Author: Ulrich W. Kulisch Publisher: Springer Science & Business Media ISBN: 3709105250 Category : Computers Languages : en Pages : 151
Book Description
The number one requirement for computer arithmetic has always been speed. It is the main force that drives the technology. With increased speed larger problems can be attempted. To gain speed, advanced processors and pro gramming languages offer, for instance, compound arithmetic operations like matmul and dotproduct. But there is another side to the computational coin - the accuracy and reliability of the computed result. Progress on this side is very important, if not essential. Compound arithmetic operations, for instance, should always deliver a correct result. The user should not be obliged to perform an error analysis every time a compound arithmetic operation, implemented by the hardware manufacturer or in the programming language, is employed. This treatise deals with computer arithmetic in a more general sense than usual. Advanced computer arithmetic extends the accuracy of the elementary floating-point operations, for instance, as defined by the IEEE arithmetic standard, to all operations in the usual product spaces of computation: the complex numbers, the real and complex intervals, and the real and complex vectors and matrices and their interval counterparts. The implementation of advanced computer arithmetic by fast hardware is examined in this book. Arithmetic units for its elementary components are described. It is shown that the requirements for speed and for reliability do not conflict with each other. Advanced computer arithmetic is superior to other arithmetic with respect to accuracy, costs, and speed.
Author: Marco Nehmeier Publisher: Springer ISBN: 3319317695 Category : Computers Languages : en Pages : 291
Book Description
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.
Author: G.V. Milovanovic Publisher: Springer Science & Business Media ISBN: 9401590869 Category : Mathematics Languages : en Pages : 518
Book Description
This volume is dedicated to the late Professor Dragoslav S. Mitrinovic(1908-1995), one of the most accomplished masters in the domain of inequalities. Inequalities are to be found everywhere and play an important and significant role in almost all subjects of mathematics as well as in other areas of sciences. Professor Mitrinovic used to say: `There are no equalities, even in human life inequalities are always encountered.' This volume provides an extensive survey of the most current topics in almost all subjects in the field of inequalities, written by 85 outstanding scientists from twenty countries. Some of the papers were presented at the International Memorial Conference dedicated to Professor D.S. Mitrinovic, which was held at the University of Nis, June 20-22, 1996. Audience: This book will be of great interest to researchers in real, complex and functional analysis, special functions, approximation theory, numerical analysis and computation, and other fields, as well as to graduate students requiring the most up-to-date results.
Author: Miodrag Petković Publisher: John Wiley & Sons ISBN: 9783527401345 Category : Mathematics Languages : en Pages : 296
Book Description
The aim of this book is to present formulas and methods developed using complex interval arithmetic. While most of numerical methods described in the literature deal with real intervals and real vectors, there is no systematic study of methods in complex interval arithmetic. The book fills this gap. Several main subjects are considered: outer estimates for the range of complex functions, especially complex centered forms, the best approximations of elementary complex functions by disks, iterative methods for the inclusion by polynomial zeros including their implementation on parallel computers, the analysis of numerical stability of iterative methods by using complex interval arithmetic and numerical computation of curvilinear integrals with error bounds. Mainly new methods are presented developed over the last years, including a lot of very recent results by the authors some of which have not been published before.
Author: Tibor Csendes Publisher: Springer Science & Business Media ISBN: 9401712476 Category : Mathematics Languages : en Pages : 402
Book Description
The SCAN conference, the International Symposium on Scientific Com puting, Computer Arithmetic and Validated Numerics, takes place bian nually under the joint auspices of GAMM (Gesellschaft fiir Angewandte Mathematik und Mechanik) and IMACS (International Association for Mathematics and Computers in Simulation). SCAN-98 attracted more than 100 participants from 21 countries all over the world. During the four days from September 22 to 25, nine highlighted, plenary lectures and over 70 contributed talks were given. These figures indicate a large participation, which was partly caused by the attraction of the organizing country, Hungary, but also the effec tive support system have contributed to the success. The conference was substantially supported by the Hungarian Research Fund OTKA, GAMM, the National Technology Development Board OMFB and by the J6zsef Attila University. Due to this funding, it was possible to subsidize the participation of over 20 scientists, mainly from Eastern European countries. It is important that the possibly first participation of 6 young researchers was made possible due to the obtained support. The number of East-European participants was relatively high. These results are especially valuable, since in contrast to the usual 2 years period, the present meeting was organized just one year after the last SCAN-xx conference.
Author: Ulrich Kulisch
Author: Ulrich Kulisch
Author: Lidiya Atanassova
Author: Christian Ullrich
Author: Ulrich Kulisch
Author: Ulrich W. Kulisch
Author: Adams
Author: Marco Nehmeier
Author: G.V. Milovanovic
Author: Miodrag Petković
Author: Tibor Csendes