Lectures on Finite Precision Computations

Mathematics of Computing -- Numerical Analysis.

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Author: Francoise Chaitin-Chatelin

Publisher: SIAM

ISBN: 9780898713589

Category: Mathematics

Page: 235

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Mathematics of Computing -- Numerical Analysis.

Matrix Computations

Lectures on Finite Precision Computations, SIAM Publications, Philadelphia, PA.
The design of production software for matrix computations requires a detailed
understanding of finite precision arithmetic, see: J.W. Demmel (1984). “Underflow
 ...

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Author: Gene H. Golub

Publisher: JHU Press

ISBN: 9781421408590

Category: Mathematics

Page: 784

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The fourth edition of Gene H. Golub and Charles F. Van Loan's classic is an essential reference for computational scientists and engineers in addition to researchers in the numerical linear algebra community. Anyone whose work requires the solution to a matrix problem and an appreciation of its mathematical properties will find this book to be an indispensible tool. This revision is a cover-to-cover expansion and renovation of the third edition. It now includes an introduction to tensor computations and brand new sections on • fast transforms • parallel LU • discrete Poisson solvers • pseudospectra • structured linear equation problems • structured eigenvalue problems • large-scale SVD methods • polynomial eigenvalue problems Matrix Computations is packed with challenging problems, insightful derivations, and pointers to the literature—everything needed to become a matrix-savvy developer of numerical methods and software. The second most cited math book of 2012 according to MathSciNet, the book has placed in the top 10 for since 2005.

Quality of Numerical Software

Chaitin-Chatelin, F. and Frayssé, V. (1996) Lectures on Finite Precision
Computations. SIAM, Philadelphia. Chaitin-Chatelin, F. and Gratton, S. (1996)
Convergence of successive iteration methods in finite precision under high
nonnormality.

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Author: Ronald F. Boisvert

Publisher: Springer

ISBN: 9781504129404

Category: Computers

Page: 384

View: 969

Numerical software is central to our computerized society. It is used to control aeroplanes and bridges, operate manufacturing lines, control power plants and refineries, and analyse financial markets. Such software must be accurate, reliable, robust, efficient, easy to use, maintainable and adaptable. Quality assessment and control of numerical software is still not well understood. Although measurement is a key element, it remains difficult to assess many components of software quality and to evaluate the trade-offs between them. Fortunately, as numerical software is built upon a long established foundation of mathematical and computational knowledge, there is great potential for dramatic breakthroughs. This volume will address enabling techniques and tools such as benchmarks, testing methodologies, quality standards, metrics, and accuracy control mechanisms, and their application to software for differential equations, linear algebra, data analysis, as well as the evaluation of integrals, derivatives and elementary and special functions.

Qualitative Computing

A Computational Journey Into Nonlinearity Françoise Chatelin, Françoise Chaitin
-Chatelin ... Chaitin-Chatelin (1996) Is finite precision arithmetic useful for
Physics?, Journ. of Universal Comp. ... Lectures on Finite Precision
Computations.

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Author: Françoise Chatelin

Publisher: World Scientific

ISBN: 9789814322928

Category: Mathematics

Page: 582

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Introduction to Qualitative Computing; Hypercomputation in Dickson Algebras; Scales of Complexity and Linear Reachability; Singular Values for the Multiplication Maps; Computation Beyond Classical Logic; Complexification of the Arithmetic; Homotopic Deviation in Linear Algebra; The Discrete and the Continuous; Arithmetic in the Alternative Dickson Division Algebras; The Real and the Complex.

Enabling Technologies for Computational Science

NetSolve: A network server for solving computational science problems. Int'l. J.
Supercomput. Appl. and High Perf. Comput., 11:212–223. Chaitin-Chatelin, F.
and Frayssé, V. (1996). Lectures on Finite Precision Computations. SIAM ...

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Author: Elias N. Houstis

Publisher: Springer Science & Business Media

ISBN: 9781461545415

Category: Computers

Page: 402

View: 983

Enabling Technologies for Computational Science assesses future application computing needs, identifies research directions in problem-solving environments (PSEs), addresses multi-disciplinary environments operating on the Web, proposes methodologies and software architectures for building adaptive and human-centered PSEs, and describes the role of symbolic computing in scientific and engineering PSEs. The book also includes an extensive bibliography of over 400 references. Enabling Technologies for Computational Science illustrates the extremely broad and interdisciplinary nature of the creation and application of PSEs. Authors represent academia, government laboratories and industry, and come from eight distinct disciplines (chemical engineering, computer science, ecology, electrical engineering, mathematics, mechanical engineering, psychology and wood sciences). This breadth and diversity extends into the computer science aspects of PSEs. These papers deal with topics such as artificial intelligence, computer-human interaction, control, data mining, graphics, language design and implementation, networking, numerical analysis, performance evaluation, and symbolic computing. Enabling Technologies for Computational Science provides an assessment of the state of the art and a road map to the future in the area of problem-solving environments for scientific computing. This book is suitable as a reference for scientists from a variety of disciplines interested in using PSEs for their research.

SIAM Journal on Scientific Computing

solving systems of linear equations , in Numerical Analysis , G . Watson , ed . ,
Lectures Notes in Math . 912 , Springer ... the behavior of finite precision Lanczos
and conjugate gradient computations , SIAM J . Matrix Anal . Appl . , 13 ( 1992 ) ...

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Author:

Publisher:

ISBN: UOM:39015047828564

Category: Mathematical statistics

Page:

View: 871

SIAM Journal on Matrix Analysis and Applications

... 10 ( 1989 ) , pp . 494 - 499 . [ 6 ] F . CHAITIN - CHATELIN AND V . FRAYSSÉ ,
Lectures on Finite Precision Computations , SIAM , Philadelphia , PA , 1996 . [. 7.
] F . CHATELIN. ,. Eigenvalues. of. Matrices. ,. Wiley. ,. Chichester. ,. UK. ,. 1993.

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Author:

Publisher:

ISBN: UCAL:B4585804

Category: Electronic journals

Page:

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Computational Science for the 21st Century

... matrices in finite precision . Numerical Analysis Report No . , Manchester
Centre for Computational Mathematics . ... Chaitin - Chatelin F . and Frayssé V . (
1996 ) Lecture on Finite Precision Computations . SIAM . Chaitin - Chatelin F .
and ...

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Author: Garret J. Etgen

Publisher: John Wiley & Sons Incorporated

ISBN: STANFORD:36105022399187

Category: Computers

Page: 840

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Computational science can loosely be defined as the endeavor to develop and analyse models for the simulation and control of complex processes. This is achieved by making optimal use of computer resources and by drawing upon a variety of disciplines, techniques and theories. With the emergence of advanced computational and information technologies, computational science now has a significant impact on engineering, physical, biological, management and social sciences. The contributions in this state-of-the-art volume range from theoretical and numerical topics to practical implementations. The subject matter includes modelling, mathematical and numerical analysis, differential equations, linear algebra, optimization, domain decomposition, computational fluid dynamics, computational mechanics, elasticity, structure, computational physics and chemistry, electromagnetic, control theory and other applications. This volume is dedicated to Roland Glowinski on the occasion of his 60th birthday. It is aimed at the next generation of scientists, applied mathematicians, computer scientists, practitioners and engineers who will define computational science within the context of the challenging scientific, industrial, economic and societal problems of the 21st century.

BIT

F . Chaitin - Chatelin and V . Frayssé , Lectures on Finite Precision Computations
, SIAM , Philadelphia , PA , 1996 . 4 . J . K . Cullum and A . E . Ruehli , Method for
analyzing the stability and passivity of system models , US Patent , 6058258 ...

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Author:

Publisher:

ISBN: UOM:39015048297744

Category: Numerical analysis

Page:

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Numerical Analysis and Its Applications

Therefore a complete explanation for the "convergence" of Krylov methods in
finite precision requires to complement the classical point of view of exact
convergence (h —* 0), valid when the ... Lectures on Finite Precision
Computation. Publ.

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Author:

Publisher:

ISBN: UOM:39015058889224

Category: Numerical analysis

Page:

View: 898

Static Analysis

( CC94 ) F. Chaitin - Chatelin . Le calcul sur ordinateur à précision finie , théorie
et état de l'art . Technical Report TR / PA / 94 / 05 , CERFACS , 1994 . ( CCF96 ] F
. Chaitin - Chatelin and V. Frayss . Lectures on Finite Precision Computations .

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Author:

Publisher:

ISBN: UOM:39015049126686

Category: Computer programming

Page:

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Mathematical Reviews

Lecture Note Ser . , 331 , Cambridge Univ . Press , Cambridge , 2006 . Starting
from the ... The main objective of the paper is to show the influence of roundoff
errors due to finite precision computations . Some of the questions addressed are
 ...

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Author:

Publisher:

ISBN: UOM:39015078588616

Category: Mathematics

Page:

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Precision based Program Optimization

Lectures on Finite Precision Computations . SIAM , 1996 . [ 3 ] Luiz H. de
Figueiredo and Jorge Stolfi . Self- Validated Numerical Methods and Applications
. Brazilian Mathematics Colloquium monographs . IMPA / CNPq , Rio de Janeiro
 ...

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Author: Gary Edward Adams

Publisher:

ISBN: CORNELL:31924086361882

Category:

Page: 462

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Lastly, the thesis presents techniques for static selection of numerical formats and word lengths for each data variable and arithmetic operation in a program. A program fragment from a adaptive radar data processing computation is used to demonstrate the precision analysis and program optimizations.

Monthly Weather Review

-0.6 Braconnier , T. , 1994 : Sur le calcul de valeurs propres en précision finie .
Ph.D. dissertation , Université H. ... Chaitin - Chatelin , F. , and V. Frayssé , 1996 :
Lectures on Finite Precision Computations . SIAM , 235 pp . Chatelin , F. , 1993 ...

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Author:

Publisher:

ISBN: UIUC:30112052796395

Category: Meteorology

Page:

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Numerical Analysis

N62 279 ( CF ) Chaitin - Chatelin , F. and Fraysse , V. , Lectures on finite
precision computations , SIAM Publications , Philadelphia , PA , 1996 , 235 pp .
QA297.C417 44 ( CGGG ] Char , B. W. , K. O. Geddes , W. M. Gentlemen , and
G. H. ...

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Author: Richard L. Burden

Publisher:

ISBN: CORNELL:31924103813089

Category: Analyse numérique

Page: 847

View: 746

1. Mathematical preliminaries and error analysis -- 2. Solutions of equations in one variable -- 3. Interpolation and polynomial approximation -- 4. Numerical differentiation and integration -- 5. Initial-value problems for ordinary differential equations -- 6. Direct methods for solving linear systems -- 7. Iterative techniques in matrix algebra -- 8. Approximation theory -- 9. Approximating eigenvalues -- 10. Numerical solutions of nonlinear systems of equations -- 11. Boundary-value problems for ordinary differential equations -- 12. Numerical solutions to partial differential equations. Local Subj.

Verification Model Checking and Abstract Interpretation

Second , automatic differentiation and error series compute the same floating -
point values as the program and , additionnally , determine which roundoff errors
will significantly modify the result of ... Lectures on Finite Precision Computations
.

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Author:

Publisher:

ISBN: UOM:39015058889398

Category: Computer programs

Page:

View: 713

AMSTAT News

... F . , and Fraysee , V . Cheney , E . W . Environmetrics 81 : Selected Papers
Lectures on Finite Precision Computation 1 ... Topics Sequential Analysis and
Optimal Design Multivariate Splines Handbook for Matrix Computations 1 - 006 -
5 21 .

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Author:

Publisher:

ISBN: UOM:39015040429055

Category: Statistics

Page:

View: 465

Bibliographic Index

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Author:

Publisher:

ISBN: PSU:000063912173

Category: Bibliographical literature

Page: 26

View: 859

Journal of Economic Literature

Lectures on Finite Precision Computations . Philadelphia : SIAM . Coveyou , R .
and R . MacPherson . 1967 . " Fourier Analysis of Uniform Random Number
Generators , ” J . ACM , 14 : 1 , pp . 100 – 19 . Dahlquist , Germund and Ake
Björck ...

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Author:

Publisher:

ISBN: UCSD:31822027659267

Category: Economics

Page:

View: 434

Numerical Methods

( CF ) ( Ch ] Chaitin - Chatelin , F . and Fraysse , V . , Lectures on finite precision
computations , SIAM Publications ... and J . W . Tukey , An algorithm for the
machine calculation of complex Fourier series , Mathematics of Computation 19 ,
No .

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Author: J. Douglas Faires

Publisher: Brooks Cole

ISBN: UOM:39015041023386

Category: Numerical analysis

Page: 594

View: 231

This text emphasizes the intelligent application of approximation techniques to the type of problems that commonly occur in engineering and the physical sciences. The authors provide a sophisticated introduction to various appropriate approximation techniques; they show students why the methods work, what type of errors to expect, and when an application might lead to difficulties; and they provide information about the availability of high-quality software for numerical approximation routines The techniques covered in this text are essentially the same as those covered in the Sixth Edition of these authors' top-selling Numerical Analysis text, but the emphasis is much different. In Numerical Methods, Second Edition, full mathematical justifications are provided only if they are concise and add to the understanding of the methods. The emphasis is placed on describing each technique from an implementation standpoint, and on convincing the student that the method is reasonable both mathematically and computationally.