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Numbers and Computers
This is a book about numbers and how those numbers are represented in and operated on by computers. It is crucial that developers understand this area because the numerical operations allowed by computers, and the limitations of those operations, especially in the area of floating point math, affect virtually everything people try to do with computers. This book aims to fill this gap by exploring, in sufficient but not overwhelming detail, just what it is that computers do with numbers. Divided into two parts, the first deals with standard representations of integers and floating point numbers, while the second examines several other number representations. Details are explained thoroughly, ...
Mathematical Software - ICMS 2010
The ICMS Developer's Meeting is an international congress for which the main theme is mathematical software. The 2010 meeting was the third of a series of meetings of similar theme, the ?rst being held in Beijing, China in 2002,and the second in Castro-Urdiales, Spain in 2006. The ?eld of mathematics has numerous branches, and in each branch we ?nd that algorithms, and also implementations and applications of software s- tems, are studied. Researchers who endeavor to make such studies also have international meetings within their speci'c branches of mathematics, and these meetings have made signi'cant contributions to the ?elds in which they lie. The ICMS (International Congresseson Mathematical Software), on the other hand, is a general (not branch speci'c) meeting on mathematical software, which is held every four years, and is a rare opportunity for developers of mathematical softwarefrom di'erent branchesof mathematics, as well as mathematicians who are interested in mathematical software, to gather together.
Numerical Software Verification
This book constitutes the proceedings of the 10th International Workshop on Numerical Software Verification, NSV 2017, held in Heidelberg, Germany, in July 2017 - colocated with the International Workshop on Formal Methods for Rigorous Systems Engineering of Cyber-Physical Systems, RISE4CPS 2017, a one-time, invited-only event.The 3 full papers presented together with 3 short papers, 2 keynote abstracts and 4 invited abstracts were carefully reviewed and selected from numerous submissions.The NSV 2017 workshop is dedicated to the development of logical and mathematical techniques for the reasoning about programmability and reliability.
Applied Interval Analysis
At the core of many engineering problems is the solution of sets of equa tions and inequalities, and the optimization of cost functions. Unfortunately, except in special cases, such as when a set of equations is linear in its un knowns or when a convex cost function has to be minimized under convex constraints, the results obtained by conventional numerical methods are only local and cannot be guaranteed. This means, for example, that the actual global minimum of a cost function may not be reached, or that some global minimizers of this cost function may escape detection. By contrast, interval analysis makes it possible to obtain guaranteed approximations of the set of all the actual solutio...
Numerical Software with Result Verification
This book constitutes the thoroughly refereed post-proceedings of the Dagstuhl Seminar 03041 on Numerical Software with Result Verification held at Dagstuhl Castle, Germany, in January 2003. The 18 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.
Parallel Processing and Applied Mathematics
This book constitutes the thoroughly refereed post-proceedings of the 4th International Conference on Parallel Processing and Applied Mathematics, PPAM 2002, held in Naleczow, Poland, in September 2001. The 101 papers presented were carefully reviewed and improved during two rounds of reviewing and revision. The book offers topical sections on distributed and grid architectures, scheduling and load balancing, performance analysis and prediction, parallel non-numerical algorithms, parallel programming, tools and environments, parallel numerical algorithms, applications, and evolutionary computing and neural networks.
Experimental Algorithms
This book constitutes the refereed proceedings of the 8th International Symposium on Experimental and Efficient Algorithms, SEA 2009, held in Dortmund, Germany, in June 2009. The 23 revised full papers were carefully reviewed and selected from 64 submissions and present current research on experimental evaluation and engineering of algorithms, as well as in various aspects of computational optimization and its applications. Contributions are supported by experimental evaluation, methodological issues in the design and interpretation of experiments, the use of (meta- ) heuristics, or application-driven case studies that deepen the understanding of a problem's complexity.
The Mathematical-Function Computation Handbook
This highly comprehensive handbook provides a substantial advance in the computation of elementary and special functions of mathematics, extending the function coverage of major programming languages well beyond their international standards, including full support for decimal floating-point arithmetic. Written with clarity and focusing on the C language, the work pays extensive attention to little-understood aspects of floating-point and integer arithmetic, and to software portability, as well as to important historical architectures. It extends support to a future 256-bit, floating-point format offering 70 decimal digits of precision. Select Topics and Features: references an exceptionally...
Elementary Functions
Second Edition of successful, well-reviewed Birkhauser book, which sold 866 copies in North America Provides an up-to-date presentation by including new results, examples, and problems throughout the text The second edition adds a chapter on multiple-precision arithmetic, and new algorithms invented since 1997
