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Author: Rolf Hammer
Publisher: Springer Science & Business Media
ISBN: 3642784232
Category : Mathematics
Languages : en
Pages : 348
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Book Description
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.
Author: Rolf Hammer
Publisher: Springer Science & Business Media
ISBN: 3642784232
Category : Mathematics
Languages : en
Pages : 348
Get Book Here
Book Description
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.
Author: Rolf Hammer
Publisher: Springer Science & Business Media
ISBN: 3642796516
Category : Mathematics
Languages : en
Pages : 389
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Book Description
Our aim in writing this book was to provide an extensive set of C++ programs for solving basic numerical problems with verification of the results. This C++ Toolbox for Verified Computing I is the C++ edition of the Numerical Toolbox for Verified Computing l. The programs of the original edition were written in PASCAL-XSC, a PASCAL eXtension for Scientific Computation. Since we published the first edition we have received many requests from readers and users of our tools for a version in C++. We take the view that C++ is growing in importance in the field of numeri cal computing. C++ includes C, but as a typed language and due to its modern concepts, it is superior to C. To obtain the degree of efficiency that PASCAL-XSC provides, we used the C-XSC library. C-XSC is a C++ class library for eXtended Scientific Computing. C++ and the C-XSC library are an adequate alternative to special XSC-Ianguages such as PASCAL-XSC or ACRITH-XSC. A shareware version of the C-XSC library and the sources of the toolbox programs are freely available via anonymous ftp or can be ordered against reimbursement of expenses. The programs of this book do not require a great deal of insight into the features of C++. Particularly, object oriented programming techniques are not required.
Author: Rolf Hammer
Publisher: Springer
ISBN:
Category : Computers
Languages : en
Pages : 408
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Book Description
Theory, Algorithms, and Programs
Author: René Alt
Publisher: Springer Science & Business Media
ISBN: 3540212604
Category : Computers
Languages : en
Pages : 324
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Book Description
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.
Author: Rolf Hammer
Publisher: Springer
ISBN: 9783540571186
Category : Mathematics
Languages : en
Pages : 0
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Book Description
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.
Author: Mitsuhiro T. Nakao
Publisher: Springer Nature
ISBN: 9811376697
Category : Mathematics
Languages : en
Pages : 469
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Book Description
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.
Author: David Robert Stauffer
Publisher: Springer
ISBN: 9780387571188
Category : Technology & Engineering
Languages : en
Pages : 0
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Book Description
The simplest method of transferring data through the inputs or outputs of a silicon chip is to directly connect each bit of the datapath from one chip to the next chip. Once upon a time this was an acceptable approach. However, one aspect (and perhaps the only aspect) of chip design which has not changed during the career of the authors is Moore’s Law, which has dictated substantial increases in the number of circuits that can be manufactured on a chip. The pin densities of chip packaging technologies have not increased at the same pace as has silicon density, and this has led to a prevalence of High Speed Serdes (HSS) devices as an inherent part of almost any chip design. HSS devices are the dominant form of input/output for many (if not most) high-integration chips, moving serial data between chips at speeds up to 10 Gbps and beyond. Chip designers with a background in digital logic design tend to view HSS devices as simply complex digital input/output cells. This view ignores the complexity associated with serially moving billions of bits of data per second. At these data rates, the assumptions associated with digital signals break down and analog factors demand consideration. The chip designer who oversimplifies the problem does so at his or her own peril.
Author: Annie A.M. Cuyt
Publisher: Springer Science & Business Media
ISBN: 3642015905
Category : Computers
Languages : en
Pages : 272
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Book Description
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.
Author: Roman Wyrzykowski
Publisher: Springer
ISBN: 3540681116
Category : Computers
Languages : en
Pages : 1437
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Book Description
This book constitutes the thoroughly refereed post-conference proceedings of the 7th International Conference on Parallel Processing and Applied Mathematics, PPAM 2007, held in Gdansk, Poland, in September 2007. The 63 revised full papers of the main conference presented together with 85 revised workshop papers were carefully reviewed and selected from over 250 initial submissions. The papers are organized in topical sections on parallel/distributed architectures and mobile computing, numerical algorithms and parallel numerics, parallel and distributed non-numerical algorithms, environments and tools for as well as applications of parallel/distributed/grid computing, evolutionary computing, meta-heuristics and neural networks. The volume proceeds with the outcome of 11 workshops and minisymposia dealing with novel data formats and algorithms for dense linear algebra computations, combinatorial tools for parallel sparse matrix computations, grid applications and middleware, large scale computations on grids, models, algorithms and methodologies for grid-enabled computing environments, scheduling for parallel computing, language-based parallel programming models, performance evaluation of parallel applications on large-scale systems, parallel computational biology, high performance computing for engineering applications, and the minisymposium on interval analysis.
Author: Immanuel M. Bomze
Publisher: Springer Science & Business Media
ISBN: 1475726007
Category : Computers
Languages : en
Pages : 350
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Book Description
In recent years global optimization has found applications in many interesting areas of science and technology including molecular biology, chemical equilibrium problems, medical imaging and networks. The collection of papers in this book indicates the diverse applicability of global optimization. Furthermore, various algorithmic, theoretical developments and computational studies are presented. Audience: All researchers and students working in mathematical programming.
