Scientific Computation With Automatic Result Verification
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Scientific Computation With Automatic Result Verification
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Author : Ulrich Kulisch
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Scientific Computation With Automatic Result Verification written by Ulrich Kulisch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Scientific Computation with Result Verification has been a persevering research topic at the Institute for Applied Mathematics of Karlsruhe University for many years. A good number of meetings have been devoted to this area. The latest of these meetings was held from 30 September to 2 October, 1987, in Karlsruhe; it was co-sponsored by the GAMM Committee on "Computer Arithmetic and Scientific Computation". - - This volume combines edited versions of selected papers presented at this confer ence, including a few which were presented at a similar meeting one year earlier. The selection was made on the basis of relevance to the topic chosen for this volume. All papers are original contributions. In an appendix, we have supplied a short account of the Fortran-SC language which permits the programming of algorithms with result verification in a natural manner. The editors hope that the publication of this material as a Supplementum of Computing will further stimulate the interest of the scientific community in this important tool for Scientific Computation. In particular, we would like to make application scientists aware of its potential. The papers in the second chapter of this volume should convince them that automatic result verification may help them to design more reliable software for their particular tasks. We wish to thank all contributors for adapting their manuscripts to the goals of this volume. We are also grateful to the Publisher, Springer-Verlag of Vienna, for an efficient and quick production.
Scientific Computing With Automatic Result Verification
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Author : Adams
language : en
Publisher: Academic Press
Release Date : 1992-12-03
Scientific Computing With Automatic Result Verification written by Adams and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-12-03 with Computers categories.
Scientific Computing with Automatic Result Verification
Computer Aided Proofs In Analysis
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Author : Kenneth R. Meyer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computer Aided Proofs In Analysis written by Kenneth R. Meyer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This IMA Volume in Mathematics and its Applications COMPUTER AIDED PROOFS IN ANALYSIS is based on the proceedings of an IMA Participating Institutions (PI) Conference held at the University of Cincinnati in April 1989. Each year the 19 Participating Institutions select, through a competitive process, several conferences proposals from the PIs, for partial funding. This conference brought together leading figures in a number of fields who were interested in finding exact answers to problems in analysis through computer methods. We thank Kenneth Meyer and Dieter Schmidt for organizing the meeting and editing the proceedings. A vner Friedman Willard Miller, Jr. PREFACE Since the dawn of the computer revolution the vast majority of scientific compu tation has dealt with finding approximate solutions of equations. However, during this time there has been a small cadre seeking precise solutions of equations and rigorous proofs of mathematical results. For example, number theory and combina torics have a long history of computer-assisted proofs; such methods are now well established in these fields. In analysis the use of computers to obtain exact results has been fragmented into several schools.
Computer Arithmetic And Validity
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Author : Ulrich Kulisch
language : en
Publisher: Walter de Gruyter
Release Date : 2013-04-30
Computer Arithmetic And Validity written by Ulrich Kulisch and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-30 with Mathematics categories.
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.
Knowledge Processing With Interval And Soft Computing
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Author : Chenyi Hu
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-03
Knowledge Processing With Interval And Soft Computing written by Chenyi Hu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-03 with Computers categories.
Interval computing combined with fuzzy logic has become an emerging tool in studying artificial intelligence and knowledge processing (AIKP) applications since it models uncertainties frequently raised in the field. This book provides introductions for both interval and fuzzy computing in a very accessible style. Application algorithms covered in this book include quantitative and qualitative data mining with interval valued datasets, decision making systems with interval valued parameters, interval valued Nash games and interval weighted graphs. Successful applications in studying finance and economics, etc are also included. This book can serve as a handbook or a text for readers interested in applying interval and soft computing for AIKP.
Error Control And Adaptivity In Scientific Computing
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Author : Haydar Bulgak
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Error Control And Adaptivity In Scientific Computing written by Haydar Bulgak and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
One of the main ways by which we can understand complex processes is to create computerised numerical simulation models of them. Modern simulation tools are not used only by experts, however, and reliability has therefore become an important issue, meaning that it is not sufficient for a simulation package merely to print out some numbers, claiming them to be the desired results. An estimate of the associated error is also needed. The errors may derive from many sources: errors in the model, errors in discretization, rounding errors, etc. Unfortunately, this situation does not obtain for current packages and there is a great deal of room for improvement. Only if the error can be estimated is it possible to do something to reduce it. The contributions in this book cover many aspects of the subject, the main topics being error estimates and error control in numerical linear algebra algorithms (closely related to the concept of condition numbers), interval arithmetic and adaptivity for continuous models.
Computer Arithmetic And Self Validating Numerical Methods
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Author : Christian Ullrich
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Computer Arithmetic And Self Validating Numerical Methods written by Christian Ullrich and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Computers categories.
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.
Numerical Validation In Current Hardware Architectures
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Author : Annie A.M. Cuyt
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-24
Numerical Validation In Current Hardware Architectures written by Annie A.M. Cuyt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-24 with Computers categories.
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.
Scientific Computing Computer Arithmetic And Validated Numerics
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Author : Marco Nehmeier
language : en
Publisher: Springer
Release Date : 2016-04-08
Scientific Computing Computer Arithmetic And Validated Numerics written by Marco Nehmeier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-08 with Computers categories.
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.
Spectral Theory Computational Methods Of Sturm Liouville Problems
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Author : Don Hinton
language : en
Publisher: CRC Press
Release Date : 2021-02-27
Spectral Theory Computational Methods Of Sturm Liouville Problems written by Don Hinton and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-27 with Mathematics categories.
Presenting the proceedings of the conference on Sturm-Liouville problems held in conjunction with the 26th Barrett Memorial Lecture Series at the University of Tennessee, Knoxville, this text covers both qualitative and computational theory of Sturm-Liouville problems. It surveys questions in the field as well as describing applications and concepts.