Advances In Numerical Analysis Emphasizing Interval Data

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Advances in Numerical Analysis Emphasizing Interval Data

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Author : Tofigh Allahviranloo
Publisher : CRC Press
ISBN 13 : 1000540316
Total Pages : 135 pages
Book Rating : 4.0/5 (5 download)

Book Synopsis Advances in Numerical Analysis Emphasizing Interval Data by : Tofigh Allahviranloo

Download or read book Advances in Numerical Analysis Emphasizing Interval Data written by Tofigh Allahviranloo and published by CRC Press. This book was released on 2022-02-18 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical analysis forms a cornerstone of numeric computing and optimization, in particular recently, interval numerical computations play an important role in these topics. The interest of researchers in computations involving uncertain data, namely interval data opens new avenues in coping with real-world problems and deliver innovative and efficient solutions. This book provides the basic theoretical foundations of numerical methods, discusses key technique classes, explains improvements and improvements, and provides insights into recent developments and challenges. The theoretical parts of numerical methods, including the concept of interval approximation theory, are introduced and explained in detail. In general, the key features of the book include an up-to-date and focused treatise on error analysis in calculations, in particular the comprehensive and systematic treatment of error propagation mechanisms, considerations on the quality of data involved in numerical calculations, and a thorough discussion of interval approximation theory. Moreover, this book focuses on approximation theory and its development from the perspective of linear algebra, and new and regular representations of numerical integration and their solutions are enhanced by error analysis as well. The book is unique in the sense that its content and organization will cater to several audiences, in particular graduate students, researchers, and practitioners.

Advances in Numerical Analysis Emphasizing Interval Data

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Author : Tofigh Allahviranloo
Publisher : CRC Press
ISBN 13 : 1000540251
Total Pages : 218 pages
Book Rating : 4.0/5 (5 download)

Book Synopsis Advances in Numerical Analysis Emphasizing Interval Data by : Tofigh Allahviranloo

Download or read book Advances in Numerical Analysis Emphasizing Interval Data written by Tofigh Allahviranloo and published by CRC Press. This book was released on 2022-02-18 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical analysis forms a cornerstone of numeric computing and optimization, in particular recently, interval numerical computations play an important role in these topics. The interest of researchers in computations involving uncertain data, namely interval data opens new avenues in coping with real-world problems and deliver innovative and efficient solutions. This book provides the basic theoretical foundations of numerical methods, discusses key technique classes, explains improvements and improvements, and provides insights into recent developments and challenges. The theoretical parts of numerical methods, including the concept of interval approximation theory, are introduced and explained in detail. In general, the key features of the book include an up-to-date and focused treatise on error analysis in calculations, in particular the comprehensive and systematic treatment of error propagation mechanisms, considerations on the quality of data involved in numerical calculations, and a thorough discussion of interval approximation theory. Moreover, this book focuses on approximation theory and its development from the perspective of linear algebra, and new and regular representations of numerical integration and their solutions are enhanced by error analysis as well. The book is unique in the sense that its content and organization will cater to several audiences, in particular graduate students, researchers, and practitioners.

Numerical Analysis

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Author : Larkin Ridgway Scott
Publisher : Princeton University Press
ISBN 13 : 1400838967
Total Pages : 342 pages
Book Rating : 4.4/5 (8 download)

Book Synopsis Numerical Analysis by : Larkin Ridgway Scott

Download or read book Numerical Analysis written by Larkin Ridgway Scott and published by Princeton University Press. This book was released on 2011-04-18 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this book provides a rigorous and self-contained introduction to numerical analysis and presents the advanced mathematics that underpin industrial software, including complete details that are missing from most textbooks. Using an inquiry-based learning approach, Numerical Analysis is written in a narrative style, provides historical background, and includes many of the proofs and technical details in exercises. Students will be able to go beyond an elementary understanding of numerical simulation and develop deep insights into the foundations of the subject. They will no longer have to accept the mathematical gaps that exist in current textbooks. For example, both necessary and sufficient conditions for convergence of basic iterative methods are covered, and proofs are given in full generality, not just based on special cases. The book is accessible to undergraduate mathematics majors as well as computational scientists wanting to learn the foundations of the subject. Presents the mathematical foundations of numerical analysis Explains the mathematical details behind simulation software Introduces many advanced concepts in modern analysis Self-contained and mathematically rigorous Contains problems and solutions in each chapter Excellent follow-up course to Principles of Mathematical Analysis by Rudin

Numerical Analysis for Applied Science

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Author : Myron B. Allen, III
Publisher : John Wiley & Sons
ISBN 13 : 111924546X
Total Pages : 592 pages
Book Rating : 4.1/5 (192 download)

Book Synopsis Numerical Analysis for Applied Science by : Myron B. Allen, III

Download or read book Numerical Analysis for Applied Science written by Myron B. Allen, III and published by John Wiley & Sons. This book was released on 2019-03-19 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pragmatic and Adaptable Textbook Meets the Needs of Students and Instructors from Diverse Fields Numerical analysis is a core subject in data science and an essential tool for applied mathematicians, engineers, and physical and biological scientists. This updated and expanded edition of Numerical Analysis for Applied Science follows the tradition of its precursor by providing a modern, flexible approach to the theory and practical applications of the field. As before, the authors emphasize the motivation, construction, and practical considerations before presenting rigorous theoretical analysis. This approach allows instructors to adapt the textbook to a spectrum of uses, ranging from one-semester, methods-oriented courses to multi-semester theoretical courses. The book includes an expanded first chapter reviewing useful tools from analysis and linear algebra. Subsequent chapters include clearly structured expositions covering the motivation, practical considerations, and theory for each class of methods. The book includes over 250 problems exploring practical and theoretical questions and 32 pseudocodes to help students implement the methods. Other notable features include: A preface providing advice for instructors on using the text for a single semester course or multiple-semester sequence of courses Discussion of topics covered infrequently by other texts at this level, such as multidimensional interpolation, quasi-Newton methods in several variables, multigrid methods, preconditioned conjugate-gradient methods, finite-difference methods for partial differential equations, and an introduction to finite-element theory New topics and expanded treatment of existing topics to address developments in the field since publication of the first edition More than twice as many computational and theoretical exercises as the first edition. Numerical Analysis for Applied Science, Second Edition provides an excellent foundation for graduate and advanced undergraduate courses in numerical methods and numerical analysis. It is also an accessible introduction to the subject for students pursuing independent study in applied mathematics, engineering, and the physical and life sciences and a valuable reference for professionals in these areas.

Advances in Algebra and Analysis

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Author : V. Madhu
Publisher : Springer
ISBN 13 : 3030011208
Total Pages : 485 pages
Book Rating : 4.0/5 (3 download)

Book Synopsis Advances in Algebra and Analysis by : V. Madhu

Download or read book Advances in Algebra and Analysis written by V. Madhu and published by Springer. This book was released on 2019-01-23 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the first of two containing selected papers from the International Conference on Advances in Mathematical Sciences, Vellore, India, December 2017 - Volume I. This meeting brought together researchers from around the world to share their work, with the aim of promoting collaboration as a means of solving various problems in modern science and engineering. The authors of each chapter present a research problem, techniques suitable for solving it, and a discussion of the results obtained. These volumes will be of interest to both theoretical- and application-oriented individuals in academia and industry. Papers in Volume I are dedicated to active and open areas of research in algebra, analysis, operations research, and statistics, and those of Volume II consider differential equations, fluid mechanics, and graph theory.

Recent Developments in Numerical Methods and Software for ODEs/DAEs/PDEs

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Author : G D Byrne
Publisher : World Scientific
ISBN 13 : 9814506397
Total Pages : 220 pages
Book Rating : 4.8/5 (145 download)

Book Synopsis Recent Developments in Numerical Methods and Software for ODEs/DAEs/PDEs by : G D Byrne

Download or read book Recent Developments in Numerical Methods and Software for ODEs/DAEs/PDEs written by G D Byrne and published by World Scientific. This book was released on 1992-03-27 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ordinary differential equations (ODEs), differential-algebraic equations (DAEs) and partial differential equations (PDEs) are among the forms of mathematics most widely used in science and engineering. Each of these equation types is a focal point for international collaboration and research. This book contains papers by recognized numerical analysts who have made important contributions to the solution of differential systems in the context of realistic applications, and who now report the latest results of their work in numerical methods and software for ODEs/DAEs/PDEs. The papers address parallelization and vectorization of numerical methods, the numerical solution of ODEs/DAEs/PDEs, and the use of these numerical methods in realistic scientific and engineering applications. Contents:An Overview of Recent Developments in Numerical Methods and Software for ODEs/DAEs/PDEs (G D Byrne & W E Schiesser)Experiments with an Ordinary Differential Equation Solver in the Parallel Solution of Method of Lines Problems on a Shared memory Parallel Computer (D K Kahaner et al.)Crayfishpak: A Vectorized Fortran Package to Solve Helmholtz Equations (R A Sweet)Experiments with an Adaptive H-, P-, R-Refinement Finite Element Method for Parabolic Systems (J E Flaherty & Y Wang)Incomplete Block Factorization Preconditioners: An Implementation for Block Tridiagonal Systems (D E Salane)Fast Generation of Weights in Finite Difference Formulas (B Fornberg)Numerical Methods for Boundary Value Problems in Differential-Algebraic Equations (U M Ascher & L R Petzold)The Solution of a Co-Polymerization Model with VODE (G D Byrne)Index Readership: Applied mathematicians, engineers and numerical analysts. keywords:Software;Numerical Methods;ODEs/DAEs/PDEs;Software;Numerical Methods;Ordinary Differential Equations;Differential-Algebraic Equations;Partial Differential Equations;Scientific and Engineering Applications

Advanced Numerical and Semi-Analytical Methods for Differential Equations

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Author : Snehashish Chakraverty
Publisher : John Wiley & Sons
ISBN 13 : 1119423422
Total Pages : 256 pages
Book Rating : 4.1/5 (194 download)

Book Synopsis Advanced Numerical and Semi-Analytical Methods for Differential Equations by : Snehashish Chakraverty

Download or read book Advanced Numerical and Semi-Analytical Methods for Differential Equations written by Snehashish Chakraverty and published by John Wiley & Sons. This book was released on 2019-04-16 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examines numerical and semi-analytical methods for differential equations that can be used for solving practical ODEs and PDEs This student-friendly book deals with various approaches for solving differential equations numerically or semi-analytically depending on the type of equations and offers simple example problems to help readers along. Featuring both traditional and recent methods, Advanced Numerical and Semi Analytical Methods for Differential Equations begins with a review of basic numerical methods. It then looks at Laplace, Fourier, and weighted residual methods for solving differential equations. A new challenging method of Boundary Characteristics Orthogonal Polynomials (BCOPs) is introduced next. The book then discusses Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM), and Boundary Element Method (BEM). Following that, analytical/semi analytic methods like Akbari Ganji's Method (AGM) and Exp-function are used to solve nonlinear differential equations. Nonlinear differential equations using semi-analytical methods are also addressed, namely Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM), and Homotopy Analysis Method (HAM). Other topics covered include: emerging areas of research related to the solution of differential equations based on differential quadrature and wavelet approach; combined and hybrid methods for solving differential equations; as well as an overview of fractal differential equations. Further, uncertainty in term of intervals and fuzzy numbers have also been included, along with the interval finite element method. This book: Discusses various methods for solving linear and nonlinear ODEs and PDEs Covers basic numerical techniques for solving differential equations along with various discretization methods Investigates nonlinear differential equations using semi-analytical methods Examines differential equations in an uncertain environment Includes a new scenario in which uncertainty (in term of intervals and fuzzy numbers) has been included in differential equations Contains solved example problems, as well as some unsolved problems for self-validation of the topics covered Advanced Numerical and Semi Analytical Methods for Differential Equations is an excellent text for graduate as well as post graduate students and researchers studying various methods for solving differential equations, numerically and semi-analytically.

Analysis of Symbolic Data

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Author : Hans-Hermann Bock
Publisher : Springer Science & Business Media
ISBN 13 : 3642571557
Total Pages : 444 pages
Book Rating : 4.6/5 (425 download)

Book Synopsis Analysis of Symbolic Data by : Hans-Hermann Bock

Download or read book Analysis of Symbolic Data written by Hans-Hermann Bock and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the most recent methods for analyzing and visualizing symbolic data. It generalizes classical methods of exploratory, statistical and graphical data analysis to the case of complex data. Several benchmark examples from National Statistical Offices illustrate the usefulness of the methods. The book contains an extensive bibliography and a subject index.

Fundamentals of Engineering Numerical Analysis

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Author : Parviz Moin
Publisher : Cambridge University Press
ISBN 13 : 1139489550
Total Pages : pages
Book Rating : 4.1/5 (394 download)

Book Synopsis Fundamentals of Engineering Numerical Analysis by : Parviz Moin

Download or read book Fundamentals of Engineering Numerical Analysis written by Parviz Moin and published by Cambridge University Press. This book was released on 2010-08-23 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the original publication of this book, available computer power has increased greatly. Today, scientific computing is playing an ever more prominent role as a tool in scientific discovery and engineering analysis. In this second edition, the key addition is an introduction to the finite element method. This is a widely used technique for solving partial differential equations (PDEs) in complex domains. This text introduces numerical methods and shows how to develop, analyse, and use them. Complete MATLAB programs for all the worked examples are now available at www.cambridge.org/Moin, and more than 30 exercises have been added. This thorough and practical book is intended as a first course in numerical analysis, primarily for new graduate students in engineering and physical science. Along with mastering the fundamentals of numerical methods, students will learn to write their own computer programs using standard numerical methods.

Recent Advances in Numerical Analysis

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Author : Carl De Boor
Publisher :
ISBN 13 :
Total Pages : 270 pages
Book Rating : 4.:/5 (476 download)

Book Synopsis Recent Advances in Numerical Analysis by : Carl De Boor

Download or read book Recent Advances in Numerical Analysis written by Carl De Boor and published by . This book was released on 1978 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Advanced Arithmetic for the Digital Computer

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Author : Ulrich W. Kulisch
Publisher : Springer Science & Business Media
ISBN 13 : 3709105250
Total Pages : 151 pages
Book Rating : 4.7/5 (91 download)

Book Synopsis Advanced Arithmetic for the Digital Computer by : Ulrich W. Kulisch

Download or read book Advanced Arithmetic for the Digital Computer written by Ulrich W. Kulisch and published by Springer Science & Business Media. This book was released on 2012-09-07 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: The number one requirement for computer arithmetic has always been speed. It is the main force that drives the technology. With increased speed larger problems can be attempted. To gain speed, advanced processors and pro gramming languages offer, for instance, compound arithmetic operations like matmul and dotproduct. But there is another side to the computational coin - the accuracy and reliability of the computed result. Progress on this side is very important, if not essential. Compound arithmetic operations, for instance, should always deliver a correct result. The user should not be obliged to perform an error analysis every time a compound arithmetic operation, implemented by the hardware manufacturer or in the programming language, is employed. This treatise deals with computer arithmetic in a more general sense than usual. Advanced computer arithmetic extends the accuracy of the elementary floating-point operations, for instance, as defined by the IEEE arithmetic standard, to all operations in the usual product spaces of computation: the complex numbers, the real and complex intervals, and the real and complex vectors and matrices and their interval counterparts. The implementation of advanced computer arithmetic by fast hardware is examined in this book. Arithmetic units for its elementary components are described. It is shown that the requirements for speed and for reliability do not conflict with each other. Advanced computer arithmetic is superior to other arithmetic with respect to accuracy, costs, and speed.

Recent Advances in Computational Sciences

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Author : Palle E. T. J0rgensen
Publisher : World Scientific
ISBN 13 : 9812792384
Total Pages : 395 pages
Book Rating : 4.8/5 (127 download)

Book Synopsis Recent Advances in Computational Sciences by : Palle E. T. J0rgensen

Download or read book Recent Advances in Computational Sciences written by Palle E. T. J0rgensen and published by World Scientific. This book was released on 2008 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents state-of-the-art lectures delivered by international academic and industrial experts in the field of computational science and its education, covering a wide spectrum from theory to practice. Topics include new developments in finite element method (FEM), finite volume method and Spline theory, such as Moving Mesh Methods, Galerkin and Discontinuous Galerkin Schemes, Shape Gradient Methods, Mixed FEMs, Superconvergence techniques and Fourier spectral approximations with applications in multidimensional fluid dynamics; Maxwell equations in discrepancy media; and phase-field equations. It also discusses some interesting topics related to Stokes equations, Schrodinger equations, wavelet analysis and approximation theory. Contemporary teaching issues in curriculum reform also form an integral part of the book. This book will therefore be of significant interest and value to all graduates, research scientists and practitioners facing complex computational problems. Administrators and policymakers will find it is an addition to their mathematics curriculum reform libraries.

Recent Advances In Computational Sciences: Selected Papers From The International Workshop On Computational Sciences And Its Education

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Author : Xiaoping Shen
Publisher : World Scientific
ISBN 13 : 981447536X
Total Pages : 395 pages
Book Rating : 4.8/5 (144 download)

Book Synopsis Recent Advances In Computational Sciences: Selected Papers From The International Workshop On Computational Sciences And Its Education by : Xiaoping Shen

Download or read book Recent Advances In Computational Sciences: Selected Papers From The International Workshop On Computational Sciences And Its Education written by Xiaoping Shen and published by World Scientific. This book was released on 2008-07-31 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents state-of-the-art lectures delivered by international academic and industrial experts in the field of computational science and its education, covering a wide spectrum from theory to practice. Topics include new developments in finite element method (FEM), finite volume method and Spline theory, such as Moving Mesh Methods, Galerkin and Discontinuous Galerkin Schemes, Shape Gradient Methods, Mixed FEMs, Superconvergence techniques and Fourier spectral approximations with applications in multidimensional fluid dynamics; Maxwell equations in discrepancy media; and phase-field equations. It also discusses some interesting topics related to Stokes equations, Schrödinger equations, wavelet analysis and approximation theory. Contemporary teaching issues in curriculum reform also form an integral part of the book.This book will therefore be of significant interest and value to all graduates, research scientists and practitioners facing complex computational problems. Administrators and policymakers will find it is an addition to their mathematics curriculum reform libraries.

Explorations In Numerical Analysis: Python Edition

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Author : James V Lambers
Publisher : World Scientific
ISBN 13 : 9811227950
Total Pages : 691 pages
Book Rating : 4.8/5 (112 download)

Book Synopsis Explorations In Numerical Analysis: Python Edition by : James V Lambers

Download or read book Explorations In Numerical Analysis: Python Edition written by James V Lambers and published by World Scientific. This book was released on 2021-01-14 with total page 691 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is intended to introduce advanced undergraduate and early-career graduate students to the field of numerical analysis. This field pertains to the design, analysis, and implementation of algorithms for the approximate solution of mathematical problems that arise in applications spanning science and engineering, and are not practical to solve using analytical techniques such as those taught in courses in calculus, linear algebra or differential equations.Topics covered include computer arithmetic, error analysis, solution of systems of linear equations, least squares problems, eigenvalue problems, nonlinear equations, optimization, polynomial interpolation and approximation, numerical differentiation and integration, ordinary differential equations, and partial differential equations. For each problem considered, the presentation includes the derivation of solution techniques, analysis of their efficiency, accuracy and robustness, and details of their implementation, illustrated through the Python programming language.This text is suitable for a year-long sequence in numerical analysis, and can also be used for a one-semester course in numerical linear algebra.

INTRODUCTORY METHODS OF NUMERICAL ANALYSIS

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Author : S. S. SASTRY
Publisher : PHI Learning Pvt. Ltd.
ISBN 13 : 8120345924
Total Pages : 463 pages
Book Rating : 4.1/5 (23 download)

Book Synopsis INTRODUCTORY METHODS OF NUMERICAL ANALYSIS by : S. S. SASTRY

Download or read book INTRODUCTORY METHODS OF NUMERICAL ANALYSIS written by S. S. SASTRY and published by PHI Learning Pvt. Ltd.. This book was released on 2012-06-12 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thoroughly revised and updated text, now in its fifth edition, continues to provide a rigorous introduction to the fundamentals of numerical methods required in scientific and technological applications, emphasizing on teaching students numerical methods and in helping them to develop problem-solving skills. While the essential features of the previous editions such as References to MATLAB, IMSL, Numerical Recipes program libraries for implementing the numerical methods are retained, a chapter on Spline Functions has been added in this edition because of their increasing importance in applications. This text is designed for undergraduate students of all branches of engineering. NEW TO THIS EDITION : Includes additional modified illustrative examples and problems in every chapter. Provides answers to all chapter-end exercises. Illustrates algorithms, computational steps or flow charts for many numerical methods. Contains four model question papers at the end of the text.

American Environmentalism

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Author : J. Michael Martinez
Publisher : CRC Press
ISBN 13 : 0415633184
Total Pages : 1227 pages
Book Rating : 4.4/5 (156 download)

Book Synopsis American Environmentalism by : J. Michael Martinez

Download or read book American Environmentalism written by J. Michael Martinez and published by CRC Press. This book was released on 2013-06-20 with total page 1227 pages. Available in PDF, EPUB and Kindle. Book excerpt: Protecting the natural environment and promoting sustainability have become important objectives, but achieving such goals presents myriad challenges for even the most committed environmentalist. American Environmentalism: Philosophy, History, and Public Policy examines whether competing interests can be reconciled while developing consistent, coherent, effective public policy to regulate uses and protection of the natural environment without destroying the national economy. It then reviews a range of possible solutions. The book delves into key normative concepts that undergird American perspectives on nature by providing an overview of philosophical concepts found in the western intellectual tradition, the presuppositions inherent in neoclassical economics, and anthropocentric (human-centered) and biocentric (earth-centered) positions on sustainability. It traces the evolution of attitudes about nature from the time of the Ancient Greeks through Europeans in the Middle Ages and the Renaissance, the Enlightenment and the American Founders, the nineteenth and twentieth centuries, and up to the present. Building on this foundation, the author examines the political landscape as non-governmental organizations (NGOs), industry leaders, and government officials struggle to balance industrial development with environmental concerns. Outrageous claims, silly misrepresentations, bogus arguments, absurd contentions, and overblown prophesies of impending calamities are bandied about by many parties on all sides of the debate—industry spokespeople, elected representatives, unelected regulators, concerned citizens, and environmental NGOs alike. In lieu of descending into this morass, the author circumvents the silliness to explore the crucial issues through a more focused, disciplined approach. Rather than engage in acrimonious debate over minutiae, as so often occurs in the context of "green" claims, he recasts the issue in a way that provides a cohesive look at all sides. This effort may be quixotic, but how else to cut the Gordian knot?

Interval Computations

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Author :
Publisher :
ISBN 13 :
Total Pages : 798 pages
Book Rating : 4.3/5 (91 download)

Book Synopsis Interval Computations by :

Download or read book Interval Computations written by and published by . This book was released on 1993 with total page 798 pages. Available in PDF, EPUB and Kindle. Book excerpt: