Self Validating Numerics For Function Space Problems
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Self Validating Numerics For Function Space Problems
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Author : Edgar W. Kaucher
language : en
Publisher: Elsevier
Release Date : 2014-06-20
Self Validating Numerics For Function Space Problems written by Edgar W. Kaucher and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-20 with Mathematics categories.
Self-Validating Numerics for Function Space Problems describes the development of computational methods for solving function space problems, including differential, integral, and function equations. This seven-chapter text highlights three approaches, namely, the E-methods, ultra-arithmetic, and computer arithmetic. After a brief overview of the different self-validating approaches, this book goes on introducing the mathematical preliminaries consisting principally of fixed-point theorems and the computational context for the development of validating methods in function spaces. The subsequent chapters deals with the development and application of point of view of ultra-arithmetic and the constructs of function-space arithmetic spaces, such as spaces, bases, rounding, and approximate operations. These topics are followed by discussion of the iterative residual correction methods for function problems and the requirements of a programming language needed to make the tools and constructs of the methodology available in actual practice on a computer. The last chapter describes the techniques for adapting the methodologies to a computer, including the self-validating results for specific problems. This book will prove useful to mathematicians and advance mathematics students.
Computer Arithmetic And Self Validating Numerical Methods
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Author : Christian Ullrich
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Computer Arithmetic And Self Validating Numerical Methods written by Christian Ullrich and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Computers categories.
Notes and Reports in Mathematics in Science and Engineering, Volume VII: Computer Arithmetic and Self-Validating Numerical Methods compiles papers presented at the first international conference on "Computer Arithmetic and Self-Validating Numerical Methods, held in Basel from October 2 to 6, 1989. This book begins by providing a tutorial introduction to computer arithmetic with operations of maximum accuracy, differentiation arithmetic and enclosure methods, and programming languages for self-validating numerical methods. The rest of the chapters discuss the determination of guaranteed bounds for eigenvalues by variational methods and guaranteed inclusion of solutions of differential equations. An appendix covering the IMACS-GAMM resolution on computer arithmetic is provided at the end of this publication. This volume is recommended for researchers and professionals working on computer arithmetic and self-validating numerical methods.
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.
Defect Correction Methods
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Author : K. Böhmer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Defect Correction Methods written by K. Böhmer 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.
Ten years ago, the term "defect correction" was introduced to characterize a class of methods for the improvement of an approximate solution of an operator equation. This class includes many well-known techniques (e.g. Newton's method) but also some novel approaches which have turned out to be quite efficient. Meanwhile a large number of papers and reports, scattered over many journals and institutions, have appeared in this area. Therefore, a working conference on "Error Asymptotics and Defect Corrections" was organized by K. Bohmer, V. Pereyra and H. J. Stetter at the Mathematisches Forschungsinstitut Oberwolfach in July 1983, a meeting which aimed at bringing together a good number of the scientists who are active in this field. Altogether 26 persons attended, whose interests covered a wide spectrum from theoretical analyses to applications where defect corrections may be utilized; a list of the participants may be found in the Appendix. Most of the colleagues who presented formal lectures at the meeting agreed to publish their reports in this volume. It would be presumptuous to call this book a state-of-the-art report in defect corrections. It is rather a collection of snapshots of activities which have been going on in a number of segments on the frontiers of this area. No systematic coverage has been attempted. Some articles focus strongly on the basic concepts of defect correction; but in the majority of the contributions the defect correction ideas appear rather as instruments for the attainment of some specified goal.
Numerical Analysis Of Ordinary Differential Equations And Its Applications
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Author : Taketomo Mitsui
language : en
Publisher: World Scientific
Release Date : 1995-10-12
Numerical Analysis Of Ordinary Differential Equations And Its Applications written by Taketomo Mitsui and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-10-12 with Mathematics categories.
The book collects original articles on numerical analysis of ordinary differential equations and its applications. Some of the topics covered in this volume are: discrete variable methods, Runge-Kutta methods, linear multistep methods, stability analysis, parallel implementation, self-validating numerical methods, analysis of nonlinear oscillation by numerical means, differential-algebraic and delay-differential equations, and stochastic initial value problems.
Reliability In Computing
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Author : Ramon E. Moore
language : en
Publisher: Elsevier
Release Date : 2014-05-10
Reliability In Computing written by Ramon E. Moore and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Perspectives in Computing, Vol. 19: Reliability in Computing: The Role of Interval Methods in Scientific Computing presents a survey of the role of interval methods in reliable scientific computing, including vector arithmetic, language description, convergence, and algorithms. The selection takes a look at arithmetic for vector processors, FORTRAN-SC, and reliable expression evaluation in PASCAL-SC. Discussions focus on interval arithmetic, optimal scalar product, matrix and vector arithmetic, transformation of arithmetic expressions, development of FORTRAN-SC, and language description with examples. The text then examines floating-point standards, algorithms for verified inclusions, applications of differentiation arithmetic, and interval acceleration of convergence. The book ponders on solving systems of linear interval equations, interval least squares, existence of solutions and iterations for nonlinear equations, and interval methods for algebraic equations. Topics include interval methods for single equations, diagnosing collinearity, interval linear equations, effects of nonlinearity, and bounding the solutions. The publication is a valuable source of data for computer science experts and researchers interested in the role of interval methods in reliable scientific computing.
Numerical Methods And Applications
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Author : Todor Boyanov
language : en
Publisher: Springer
Release Date : 2007-05-15
Numerical Methods And Applications written by Todor Boyanov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-15 with Computers categories.
This book constitutes the thoroughly refereed post-proceedings of NMA 2006 held in Borovets, Bulgaria. Coverage in the 84 revised full papers includes numerical methods for hyperbolic problems, robust preconditioning solution methods, metaheuristics for optimization problems, uncertain/control systems and reliable numerics, interpolation and quadrature processes, and large-scale computations in environmental modeling.
Accurate Scientific Computations
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Author : Willard L. Miranker
language : en
Publisher: Springer Science & Business Media
Release Date : 1986-09
Accurate Scientific Computations written by Willard L. Miranker 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 1986-09 with Mathematics categories.
Mathematics of Computing -- Numerical Analysis.
Modern Map Methods In Particle Beam Physics
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Author :
language : en
Publisher: Academic Press
Release Date : 1999-09-22
Modern Map Methods In Particle Beam Physics written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09-22 with Science categories.
Advances in Imaging & Electron Physics merges two long-running serials--Advances in Electronics & Electron Physics and Advances in Optical & Electron Microscopy. The series features extended articles on the physics of electron devices (especially semiconductor devices), particle optics at high and low energies, microlithography, image science and digital image processing, electromagnetic wave propagation, electron microscopy, and the computing methods used in all these domains.
Interval Analysis
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Author : Günter Mayer
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-04-10
Interval Analysis written by Günter Mayer and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-10 with Mathematics categories.
This self-contained text is a step-by-step introduction and a complete overview of interval computation and result verification, a subject whose importance has steadily increased over the past many years. The author, an expert in the field, gently presents the theory of interval analysis through many examples and exercises, and guides the reader from the basics of the theory to current research topics in the mathematics of computation. Contents Preliminaries Real intervals Interval vectors, interval matrices Expressions, P-contraction, ε-inflation Linear systems of equations Nonlinear systems of equations Eigenvalue problems Automatic differentiation Complex intervals