Download or read book Perspectives on Enclosure Methods written by Ulrich Kulisch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Computer Arithmetic and Enclosure Methods written by Lidiya Atanassova and published by North Holland. This book was released on 1992 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Download or read book Computer Arithmetic and Validity written by Ulrich Kulisch and published by Walter de Gruyter. This book was released on 2013-04-30 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Advanced Arithmetic for the Digital Computer written by Ulrich W. Kulisch and published by Springer Science & Business Media. This book was released on 2012-09-07 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Scientific Computing with Automatic Result Verification written by Adams and published by Academic Press. This book was released on 1992-12-03 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientific Computing with Automatic Result Verification
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.
Download or read book Recent Progress in Inequalities written by G.V. Milovanovic and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Complex Interval Arithmetic and Its Applications written by Miodrag Petković and published by John Wiley & Sons. This book was released on 1998 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Developments in Reliable Computing written by Tibor Csendes and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Numerical Infinities and Infinitesimals in Optimization written by Yaroslav D. Sergeyev and published by Springer Nature. This book was released on 2022-07-05 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a friendly introduction to the paradigm and proposes a broad panorama of killing applications of the Infinity Computer in optimization: radically new numerical algorithms, great theoretical insights, efficient software implementations, and interesting practical case studies. This is the first book presenting to the readers interested in optimization the advantages of a recently introduced supercomputing paradigm that allows to numerically work with different infinities and infinitesimals on the Infinity Computer patented in several countries. One of the editors of the book is the creator of the Infinity Computer, and another editor was the first who has started to use it in optimization. Their results were awarded by numerous scientific prizes. This engaging book opens new horizons for researchers, engineers, professors, and students with interests in supercomputing paradigms, optimization, decision making, game theory, and foundations of mathematics and computer science. “Mathematicians have never been comfortable handling infinities... But an entirely new type of mathematics looks set to by-pass the problem... Today, Yaroslav Sergeyev, a mathematician at the University of Calabria in Italy solves this problem... ” MIT Technology Review “These ideas and future hardware prototypes may be productive in all fields of science where infinite and infinitesimal numbers (derivatives, integrals, series, fractals) are used.” A. Adamatzky, Editor-in-Chief of the International Journal of Unconventional Computing. “I am sure that the new approach ... will have a very deep impact both on Mathematics and Computer Science.” D. Trigiante, Computational Management Science. “Within the grossone framework, it becomes feasible to deal computationally with infinite quantities, in a way that is both new (in the sense that previously intractable problems become amenable to computation) and natural”. R. Gangle, G. Caterina, F. Tohmé, Soft Computing. “The computational features offered by the Infinity Computer allow us to dynamically change the accuracy of representation and floating-point operations during the flow of a computation. When suitably implemented, this possibility turns out to be particularly advantageous when solving ill-conditioned problems. In fact, compared with a standard multi-precision arithmetic, here the accuracy is improved only when needed, thus not affecting that much the overall computational effort.” P. Amodio, L. Brugnano, F. Iavernaro & F. Mazzia, Soft Computing
Download or read book Interval Analysis written by Günter Mayer and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-04-10 with total page 625 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained text is a step-by-step introduction and a complete overview of interval computation and result verification, a subject whose importance has steadily increased over the past many years. The author, an expert in the field, gently presents the theory of interval analysis through many examples and exercises, and guides the reader from the basics of the theory to current research topics in the mathematics of computation. Contents Preliminaries Real intervals Interval vectors, interval matrices Expressions, P-contraction, ε-inflation Linear systems of equations Nonlinear systems of equations Eigenvalue problems Automatic differentiation Complex intervals
Download or read book Validation Numerics written by R. Albrecht and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this book give a comprehensive overview on the whole field of validated numerics. The problems covered include simultaneous systems of linear and nonlinear equations, differential and integral equations and certain applications from technical sciences. Furthermore some papers which improve the tools are included. The book is a must for scientists working in numerical analysis, computer science and in technical fields.
Download or read book Modern Map Methods in Particle Beam Physics written by and published by Academic Press. This book was released on 1999-09-22 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Imaging & Electron Physics merges two long-running serials--Advances in Electronics & Electron Physics and Advances in Optical & Electron Microscopy. The series features extended articles on the physics of electron devices (especially semiconductor devices), particle optics at high and low energies, microlithography, image science and digital image processing, electromagnetic wave propagation, electron microscopy, and the computing methods used in all these domains.
Download or read book Nonlinear Hyperbolic Problems Theoretical Applied and Computational Aspects written by Andrea Donato and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 623 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Rigorous Global Search Continuous Problems written by R. Baker Kearfott and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work grew out of several years of research, graduate seminars and talks on the subject. It was motivated by a desire to make the technology accessible to those who most needed it or could most use it. It is meant to be a self-contained introduction, a reference for the techniques, and a guide to the literature for the underlying theory. It contains pointers to fertile areas for future research. It also serves as introductory documentation for a Fortran 90 software package for nonlinear systems and global optimization. The subject of the monograph is deterministic, automatically verified or r- orous methods. In such methods, directed rounding and computational fix- point theory are combined with exhaustive search (branch and bound) te- niques. Completion of such an algorithm with a list of solutions constitutes a rigorous mathematical proof that all of the solutions within the original search region are within the output list. The monograph is appropriate as an introduction to research and technology in the area, as a desk reference, or as a graduate-level course reference. Kno- edge of calculus, linear algebra, and elementary numerical analysis is assumed.
Download or read book Numerical Toolbox for Verified Computing I written by Rolf Hammer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: As suggested by the title of this book Numerical Toolbox for Verified Computing, we present an extensive set of sophisticated tools to solve basic numerical problems with a verification of the results. We use the features of the scientific computer language PASCAL-XSC to offer modules that can be combined by the reader to his/her individual needs. Our overriding concern is reliability - the automatic verification of the result a computer returns for a given problem. All algorithms we present are influenced by this central concern. We must point out that there is no relationship between our methods of numerical result verification and the methods of program verification to prove the correctness of an imple~entation for a given algorithm. This book is the first to offer a general discussion on • arithmetic and computational reliability, • analytical mathematics and verification techniques, • algorithms, and • (most importantly) actual implementations in the form of working computer routines. Our task has been to find the right balance among these ingredients for each topic. For some topics, we have placed a little more emphasis on the algorithms. For other topics, where the mathematical prerequisites are universally held, we have tended towards more in-depth discussion of the nature of the computational algorithms, or towards practical questions of implementation. For all topics, we present exam ples, exercises, and numerical results demonstrating the application of the routines presented.
