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This self-contained treatment offers a systematic development of the theory of iterative methods. Its focal point resides in an analysis of the convergence properties of the successive overrelaxation (SOR) method, as applied to a linear system with a consistently ordered matrix. The text explores the convergence properties of the SOR method and related techniques in terms of the spectral radii of the associated matrices as well as in terms of certain matrix norms. Contents include a review of matrix theory and general properties of iterative methods; SOR method and stationary modified SOR method for consistently ordered matrices; nonstationary methods; generalizations of SOR theory and variants of method; second-degree methods, alternating direction-implicit methods, and a comparison of methods. 1971 edition.

Tremendous progress has been made in the scientific and engineering disciplines regarding the use of iterative methods for linear systems. The size and complexity of linear and nonlinear systems arising in typical applications has grown, meaning that using direct solvers for the three-dimensional models of these problems is no longer effective. At the same time, parallel computing, becoming less expensive and standardized, has penetrated these application areas. Iterative methods are easier than direct solvers to implement on parallel computers but require approaches and solution algorithms that are different from classical methods. This second edition gives an in-depth, up-to-date view of practical algorithms for solving large-scale linear systems of equations, including a wide range of the best methods available today. A new chapter on multigrid techniques has been added, whilst material throughout has been updated, removed or shortened. Numerous exercises have been added, as well as an updated and expanded bibliography.

Iterative Algebra and Dynamic Modeling links together the use of technology (Excel spreadsheets, Stella modeling software) and modern mathematical techniques to explore the interaction of algebra (at the pre-calculus level) with computer and graphing calculator technology. This book was developed to teach modern applications of mathematics at an introductory level. It is based on the authors well-received teacher-training workshops using the materials.

Iterative methods are an important and fundamental class of solution algorithms that are used by scientists and engineers. Their applications can be found in diverse fields of science, engineering and technology, for example, computational fluid dynamics, queuing and communication problems, and image and signal processing. Because of the rapid evolution of the development of this field, as well as the fact that iterative methods are not often developed in a generic form for general applications, there is a lack of published materials that treat the topic properly and fully. These lectures from the Winter School on Iterative Methods in Scientific Computing and their Applications aims to bridge such gap in the literature. The book contains the nine series of lectures taken from the school and is divided into three main parts: Basic Theory (Chapters 1-4), Preconditioning (Chapters 5-6), and Applications (Chapters 7-9). This book provides an excellent overview of state-of-the-art of the field as well as being a general introduction for beginners. It will prove useful to researchers, practitioners and engineers interested in practising scientific computing.

Tremendous progress has been made in the scientific and engineering disciplines regarding the use of iterative methods for linear systems. The size and complexity of linear and nonlinear systems arising in typical applications has grown, meaning that using direct solvers for the three-dimensional models of these problems is no longer effective. At the same time, parallel computing, becoming less expensive and standardized, has penetrated these application areas. Iterative methods are easier than direct solvers to implement on parallel computers but require approaches and solution algorithms that are different from classical methods. This second edition gives an in-depth, up-to-date view of practical algorithms for solving large-scale linear systems of equations, including a wide range of the best methods available today. A new chapter on multigrid techniques has been added, whilst material throughout has been updated, removed or shortened. Numerous exercises have been added, as well as an updated and expanded bibliography.

This new and up-to-date book - by a leading authority in the field - examines an advanced set of numerical methods and algorithms that may be used to solve large-scale, complex problems on computers with massive parallel processing capabilities. Drawing on his many years of research, the author uses a wealth of practical applications to illuminate his presentation of theory. This book is a valuable reference for professionals in the fields of computer science and applied mathematics, and engineers interested in problems involving numerical analysis and parallel computing.

Iterative Algebra and Dynamic Modeling links together the use of technology (Excel spreadsheets, Stella modeling software) and modern mathematical techniques to explore the interaction of algebra (at the pre-calculus level) with computer and graphing calculator technology. This book was developed to teach modern applications of mathematics at an introductory level. It is based on the authors well-received teacher-training workshops using the materials.

Large linear systems of equations arise in most scientific problems where mathematical models are used. The most efficient methods for solving these equations are iterative methods. The first part of this book contains basic and classical material from the study of linear algebra and numerical linear algebra. The second half of the book is unique among books on this topic, because it is devoted to the construction of preconditioners and iterative acceleration methods of the conjugate gradient type. This book is for graduate students and researchers in numerical analysis and applied mathematics.

This monograph gives an introductory treatment of the most important iterative methods for constructing fixed points of nonlinear contractive type mappings. For each iterative method considered, it summarizes the most significant contributions in the area by presenting some of the most relevant convergence theorems. It also presents applications to the solution of nonlinear operator equations as well as the appropriate error analysis of the main iterative methods.

This monograph gives an introductory treatment of the most important iterative methods for constructing fixed points of nonlinear contractive type mappings. For each iterative method considered, it summarizes the most significant contributions in the area by presenting some of the most relevant convergence theorems. It also presents applications to the solution of nonlinear operator equations as well as the appropriate error analysis of the main iterative methods.

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Large linear systems of equations arise in most scientific problems where mathematical models are used. The most efficient methods for solving these equations are iterative methods. The first part of this book contains basic and classical material from the study of linear algebra and numerical linear algebra. The second half of the book is unique among books on this topic, because it is devoted to the construction of preconditioners and iterative acceleration methods of the conjugate gradient type. This book is for graduate students and researchers in numerical analysis and applied mathematics.

This new and up-to-date book - by a leading authority in the field - examines an advanced set of numerical methods and algorithms that may be used to solve large-scale, complex problems on computers with massive parallel processing capabilities. Drawing on his many years of research, the author uses a wealth of practical applications to illuminate his presentation of theory. This book is a valuable reference for professionals in the fields of computer science and applied mathematics, and engineers interested in problems involving numerical analysis and parallel computing.

Iterative Solution of Nonlinear Equations in Several Variables provides a survey of the theoretical results on systems of nonlinear equations in finite dimension and the major iterative methods for their computational solution. Originally published in 1970, it offers a research-level presentation of the principal results known at that time. Although the field has developed since the book originally appeared, it remains a major background reference for the literature before 1970. In particular, Part II contains the only relatively complete introduction to the existence theory for finite-dimensional nonlinear equations from the viewpoint of computational mathematics. Over the years semilocal convergence results have been obtained for various methods, especially with an emphasis on error bounds for the iterates. The results and proof techniques introduced here still represent a solid basis for this topic.

Using statistical research and case studies, the author presents the most convincing case ever made for iterative development. He offers a concise summary of the key ideas that drive all agile and iterative processes, with the details of four noteworthy iterative methods: Scrum, XP, RUP, and Evo.

An ideal textbook for instructional designers in training, Real World Instructional Design emphasizes the collaborative, iterative nature of instructional design. Positing instructional design as a process of simultaneous rather than sequential tasks with learner-centered outcomes, this volume engages with the essential building blocks of systematically designed instruction: learner needs and characteristics, goals and objectives, instructional activities, assessments, and formative evaluations. Key features include a Designer’s Toolkit that includes tips and approaches that practitioners use in their work; vignettes and narrative case studies that illustrate the complexities and iterative nature of instructional design; and forms, templates, and questionnaires to support students in applying the chapter content. With updated examples, this streamlined second edition presents a timeless approach to instructional design.

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Designing Machine Learning Systems: An Iterative Process for Production-Ready Applications, brand new

An ideal textbook for instructional designers in training, Real World Instructional Design emphasizes the collaborative, iterative nature of instructional design. Positing instructional design as a process of simultaneous rather than sequential tasks with learner-centered outcomes, this volume engages with the essential building blocks of systematically designed instruction: learner needs and characteristics, goals and objectives, instructional activities, assessments, and formative evaluations. Key features include a Designer’s Toolkit that includes tips and approaches that practitioners use in their work; vignettes and narrative case studies that illustrate the complexities and iterative nature of instructional design; and forms, templates, and questionnaires to support students in applying the chapter content. With updated examples, this streamlined second edition presents a timeless approach to instructional design.