Numerical Software With Guaranteed Results
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Numerical Software With Result Verification
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Author : René Alt
language : en
Publisher: Springer
Release Date : 2004-02-12
Numerical Software With Result Verification written by René Alt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-02-12 with Computers categories.
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.
Proceedings Of The 1981 Army Numerical Analysis And Computers Conference
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Author :
language : en
Publisher:
Release Date : 1981
Proceedings Of The 1981 Army Numerical Analysis And Computers Conference written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.
Proceedings Of The Army Numerical And Computers Analysis Conference
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Author :
language : en
Publisher:
Release Date : 1981
Proceedings Of The Army Numerical And Computers Analysis Conference written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Computers categories.
Reliable Implementation Of Real Number Algorithms Theory And Practice
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Author : Peter Hertling
language : en
Publisher: Springer
Release Date : 2008-08-06
Reliable Implementation Of Real Number Algorithms Theory And Practice written by Peter Hertling and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-06 with Computers categories.
A large amount of the capacity of today’s computers is used for computations that can be described as computations involving real numbers. In this book, the focus is on a problem arising particularly in real number computations: the problem of veri?edor reliablecomputations. Since real numbersare objects c- taining an in?nite amount of information, they cannot be represented precisely on a computer. This leads to the well-known problems caused by unveri?ed - plementations of real number algorithms using ?nite precision. While this is t- ditionally seen to be a problem in numerical mathematics, there are also several scienti?c communities in computer science that are dealing with this problem. This book is a follow-up of the Dagstuhl Seminar 06021 on “Reliable Imp- mentation of Real Number Algorithms: Theory and Practice,” which took place January 8–13, 2006. It was intended to stimulate an exchange of ideas between the di?erent communities that deal with the problem of reliable implementation of real number algorithms either from a theoretical or from a practical point of view. Forty-eight researchers from many di?erent countries and many di?erent disciplines gathered in the castle of Dagstuhl to exchange views and ideas, in a relaxed atmosphere. The program consisted of 35 talks of 30 minutes each, and of three evening sessions with additional presentations and discussions. There were also lively discussions about di?erent theoretical models and practical - proaches for reliable real number computations.
Mathematical Software
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Author : John R. Rice
language : en
Publisher: Academic Press
Release Date : 2014-05-27
Mathematical Software written by John R. Rice and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-27 with Mathematics categories.
Mathematical Software deals with software designed for mathematical applications such as Fortran, CADRE, SQUARS, and DESUB. The distribution and sources of mathematical software are discussed, along with number representation and significance monitoring. User-modifiable software and non-standard arithmetic programs are also considered. Comprised of nine chapters, this volume begins with a historical background in the form of a chronological list of events that trace the development of computing in general and mathematical software in particular. The next chapter examines where and how mathematical software is being created and how it is being disseminated to eventual consumers. A number of important shortcomings are identified. The future of mathematical software and the challenges facing mathematical software are then discussed. Subsequent chapters focus on the point of view of people outside the professional community of mathematical software; the monitoring of significance in computation and its relation to number representation; libraries of mathematical software; and the automation of numerical analysis. Eleven algorithms for numerical quadrature are also compared. This book should be of considerable interest to students and specialists in the fields of mathematics and computer science.
Proceedings
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Author :
language : en
Publisher:
Release Date : 1981
Proceedings written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Computer programs categories.
Lectures On Numerical Mathematics
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Author : H. Rutishauser
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lectures On Numerical Mathematics written by H. Rutishauser 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.
The present book is an edition of the manuscripts to the courses "Numerical Methods I" and "Numerical Mathematics I and II" which Professor H. Rutishauser held at the E.T.H. in Zurich. The first-named course was newly conceived in the spring semester of 1970, and intended for beginners, while the two others were given repeatedly as elective courses in the sixties. For an understanding of most chapters the funda mentals of linear algebra and calculus suffice. In some places a little complex variable theory is used in addition. However, the reader can get by without any knowledge of functional analysis. The first seven chapters discuss the direct solution of systems of linear equations, the solution of nonlinear systems, least squares prob lems, interpolation by polynomials, numerical quadrature, and approxima tion by Chebyshev series and by Remez' algorithm. The remaining chapters include the treatment of ordinary and partial differential equa tions, the iterative solution of linear equations, and a discussion of eigen value problems. In addition, there is an appendix dealing with the qd algorithm and with an axiomatic treatment of computer arithmetic.
Software Verification
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Author : Maria Christakis
language : en
Publisher: Springer Nature
Release Date : 2020-12-05
Software Verification written by Maria Christakis and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-05 with Computers categories.
This book constitutes the refereed proceedings of the 12th International Conference on Verified Software, VSTTE 2020, and the 13th International Workshop on Numerical Software Verification, NSV 2020, held in Los Angeles, CA, USA, in July 2020. Due to COVID-19 pandemic the conference was held virtually. The 13 papers presented in this volume were carefully reviewed and selected from 21 submissions. The papers describe large-scale verification efforts that involve collaboration, theory unification, tool integration, and formalized domain knowledge as well as novel experiments and case studies evaluating verification techniques and technologies. The conference was co-located with the 32nd International Conference on Computer-Aided Verification (CAV 2020).
Masters Theses In The Pure And Applied Sciences
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Author : Wade H. Shafer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Masters Theses In The Pure And Applied Sciences written by Wade H. Shafer 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 Science categories.
Masters Theses in the Pure and Applied Sciences was first conceived, published, and disseminated by the Center for Information and Numerical Data Analysis and Synthesis (CINDAS) * at Purdue University in 1 957, starting its coverage of theses with the academic year 1955. Beginning with Volume 13, the printing and dissemination phases of the activity were transferred to University Microfilms/Xerox of Ann Arbor, Michigan, with the thought that such an arrangement would be more beneficial to the academic and general scientific and technical community. After five years of this joint undertaking we had concluded that it was in the interest of all con cerned if the printing and distribution of the volumes were handled by an interna tional publishing house to assure improved service and broader dissemination. Hence, starting with Volume 18, Masters Theses in the Pure and Applied Sciences has been disseminated on a worldwide basis by Plenum Publishing Cor poration of New York, and in the same year the coverage was broadened to include Canadian universities. All back issues can also be ordered from Plenum. We have reported in Volume 36 (thesis year 1991) a total of 11,024 thesis titles from 23 Canadian and 161 United States universities. We are sure that this broader base for these titles reported will greatly enhance the value of this important annual reference work. While Volume 36 reports theses submitted in 1991, on occasion, certain univer sities do report theses submitted in previous years but not reported at the time.
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.