Scientific Computing And Validated Numerics
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Scientific Computing Validated Numerics Interval Methods
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Author : Walter Krämer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Scientific Computing Validated Numerics Interval Methods written by Walter Krämer 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 2013-04-17 with Computers categories.
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
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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.
Scientific Computing And Validated Numerics
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Author : G. Alefeld
language : en
Publisher: De Gruyter Akademie Forschung
Release Date : 1996
Scientific Computing And Validated Numerics written by G. Alefeld and has been published by De Gruyter Akademie Forschung this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
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.
Validated Numerics
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Author : Warwick Tucker
language : en
Publisher: Princeton University Press
Release Date : 2023-06-06
Validated Numerics written by Warwick Tucker and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-06 with Computers categories.
""Validated Numerics" contains introductory material on interval arithmetic and rigorous computations that is easily accessible to students with little background in mathematics and computer programming. I am not aware of any other book like it. The exercises and computer labs make it ideal for the classroom, and the references offer a good starting point for readers trying to gain deeper knowledge in this area."--Zbigniew Galias, AGH University of Science and Technology, Krakw -- "A significant contribution, particularly since there are not many texts in this area. "Validated Numerics" will be read by those interested in interval arithmetic, numerical analysis, and ways to make computer simulations more robust and less susceptible to errors. It is well written and well organized."--A. J. Meir, Auburn University.
Special Issue Scientific Computing Computer Arithmetic And Validated Numerics
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Author : G. Alefeld
language : en
Publisher:
Release Date : 2007
Special Issue Scientific Computing Computer Arithmetic And Validated Numerics written by G. Alefeld and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
Numerical Validation In Current Hardware Architectures
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Author : Annie A.M. Cuyt
language : en
Publisher: Springer
Release Date : 2009-04-28
Numerical Validation In Current Hardware Architectures written by Annie A.M. Cuyt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-28 with Computers categories.
This book constitutes the thoroughly refereed post-proceedings of the Dagstuhl Seminar 08021 on Numerical Validation in Current Hardware Architectures held at Dagstuhl Castle, Germany, in January 2008. The 16 revised full papers presented were selected during two rounds of reviewing and improvements. The papers are organized in topical sections on languages, software systems and tools, new verification techniques based on interval arithmetic, applications in science and engineering, and novel approaches to verification.
Numerical Verification Methods And Computer Assisted Proofs For Partial Differential Equations
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Author : Mitsuhiro T. Nakao
language : en
Publisher: Springer Nature
Release Date : 2019-11-11
Numerical Verification Methods And Computer Assisted Proofs For Partial Differential Equations written by Mitsuhiro T. Nakao and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-11 with Mathematics categories.
In the last decades, various mathematical problems have been solved by computer-assisted proofs, among them the Kepler conjecture, the existence of chaos, the existence of the Lorenz attractor, the famous four-color problem, and more. In many cases, computer-assisted proofs have the remarkable advantage (compared with a “theoretical” proof) of additionally providing accurate quantitative information. The authors have been working more than a quarter century to establish methods for the verified computation of solutions for partial differential equations, mainly for nonlinear elliptic problems of the form -∆u=f(x,u,∇u) with Dirichlet boundary conditions. Here, by “verified computation” is meant a computer-assisted numerical approach for proving the existence of a solution in a close and explicit neighborhood of an approximate solution. The quantitative information provided by these techniques is also significant from the viewpoint of a posteriori error estimates for approximate solutions of the concerned partial differential equations in a mathematically rigorous sense. In this monograph, the authors give a detailed description of the verified computations and computer-assisted proofs for partial differential equations that they developed. In Part I, the methods mainly studied by the authors Nakao and Watanabe are presented. These methods are based on a finite dimensional projection and constructive a priori error estimates for finite element approximations of the Poisson equation. In Part II, the computer-assisted approaches via eigenvalue bounds developed by the author Plum are explained in detail. The main task of this method consists of establishing eigenvalue bounds for the linearization of the corresponding nonlinear problem at the computed approximate solution. Some brief remarks on other approaches are also given in Part III. Each method in Parts I and II is accompanied by appropriate numerical examples that confirm the actual usefulness of the authors’ methods. Also in some examples practical computer algorithms are supplied so that readers can easily implement the verification programs by themselves.
Validation Numerics
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Author : R. Albrecht
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Validation Numerics written by R. Albrecht 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 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.
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
Large Scale Scientific Computing
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Author : Ivan Lirkov
language : en
Publisher: Springer
Release Date : 2006-02-15
Large Scale Scientific Computing written by Ivan Lirkov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-15 with Computers categories.
This book constitutes the thoroughly refereed post-proceedings of the 5th International Conference on Large-Scale Scientific Computations, LSSC 2005, held in Sozopol, Bulgaria in June 2005. The 75 revised full papers presented together with five invited papers were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections.