Numerical Approximation Methods

Numerical Methods and Methods of Approximation in Science and Engineering prepares students and other readers for advanced studies involving applied numerical and computational analysis. Focused on bu

Most physical problems can be written in the form of mathematical equations (differential, integral, etc.). Mathematicians have always sought to find analytical solutions to the equations encountered

Written in an easy-to-understand manner, this comprehensive textbook brings together both basic and advanced concepts of numerical methods in a single volume. Important topics including error analysis, nonlinear equations, systems of linear equations, interpolation and interpolation for Equal intervals and bivariate interpolation are discussed comprehensively. The textbook is written to cater to the needs of undergraduate students of mathematics, computer science, mechanical engineering, civil engineering and information technology for a course on numerical methods/numerical analysis. The text simplifies the understanding of the concepts through exercises and practical examples. Pedagogical features including solved examples and unsolved exercises are interspersed throughout the book for better understanding.

Numerical Methods: Using MATLAB, Fourth Edition, provides a clear, rigorous introduction to a wide range of numerical methods and their practical applications. The authors integrate MATLAB with numeri

This book summarizes recent advances in applying saddlepoint approximation methods to financial engineering. It addresses pricing exotic financial derivatives and calculating risk contributions to Val

Although numerical approximation and statistical inference are traditionally covered as entirely separate subjects, they are intimately connected through the common purpose of making estimations with partial information. This book explores these connections from a game and decision theoretic perspective, showing how they constitute a pathway to developing simple and general methods for solving fundamental problems in both areas. It illustrates these interplays by addressing problems related to numerical homogenization, operator adapted wavelets, fast solvers, and Gaussian processes. This perspective reveals much of their essential anatomy and greatly facilitates advances in these areas, thereby appearing to establish a general principle for guiding the process of scientific discovery. This book is designed for graduate students, researchers, and engineers in mathematics, applied mathematics, and computer science, and particularly researchers interested in drawing on and developing this

Mathematical and numerical modelling of the human cardiovascular system has attracted remarkable research interest due to its intrinsic mathematical difficulty and the increasing impact of cardiovascular diseases worldwide. This book addresses the two principal components of the cardiovascular system: arterial circulation and heart function. It systematically describes all aspects of the problem, stating the basic physical principles, analysing the associated mathematical models that comprise PDE and ODE systems, reviewing sound and efficient numerical methods for their approximation, and simulating both benchmark problems and clinically inspired problems. Mathematical modelling itself imposes tremendous challenges, due to the amazing complexity of the cardiovascular system and the need for computational methods that are stable, reliable and efficient. The final part is devoted to control and inverse problems, including parameter estimation, uncertainty quantification and the developmen

Elementary yet rigorous, this concise treatment explores practical numerical methods for solving very general two-point boundary-value problems. The approach is directed toward students with a knowled

This self-contained, systematic treatment of multivariate approximation begins with classical linear approximation, and moves on to contemporary nonlinear approximation. It covers substantial new developments in the linear approximation theory of classes with mixed smoothness, and shows how it is directly related to deep problems in other areas of mathematics. For example, numerical integration of these classes is closely related to discrepancy theory and to nonlinear approximation with respect to special redundant dictionaries, and estimates of the entropy numbers of classes with mixed smoothness are closely related to (in some cases equivalent to) the Small Ball Problem from probability theory. The useful background material included in the book makes it accessible to graduate students. Researchers will find that the many open problems in the theory outlined in the book provide helpful directions and guidance for their own research in this exciting and active area.

Previous editions of this popular textbook offered an accessible and practical introduction to numerical analysis. An Introduction to Numerical Methods: A MATLAB® Approach, Fourth Edition continues to

NUMGE 2018 is the ninth in a series of conferences on Numerical Methods in Geotechnical Engineering organized by the ERTC7 under the auspices of the International Society for Soil Mechanics and Geotec

NUMGE 2018 is the ninth in a series of conferences on Numerical Methods in Geotechnical Engineering organized by the ERTC7 under the auspices of the International Society for Soil Mechanics and Geotec

NUMGE 2018 is the ninth in a series of conferences on Numerical Methods in Geotechnical Engineering organized by the ERTC7 under the auspices of the International Society for Soil Mechanics and

This book mainly focuses on MOR techniques for the first and second order descriptor systems. The book also provides mathematical algorithms for implementing them in real-world applications. This book

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 diff

Exploration seismology uses seismic imaging to form detailed images of the Earth's interior, enabling the location of likely petroleum targets. Due to the size of seismic datasets, sophisticated numerical algorithms are required. This book provides a technical guide to the essential algorithms and computational aspects of data processing, covering the theory and methods of seismic imaging. The first part introduces an extensive online library of MATLAB® seismic data processing codes maintained by the CREWES project at the University of Calgary. Later chapters then focus on digital signal theory and relevant aspects of wave propagation and seismic modelling, followed by deconvolution and seismic migration methods. Presenting a rigorous explanation of how to construct seismic images, it provides readers with practical tools and codes to pursue research projects and analyses. It is ideal for advanced students and researchers in applied geophysics, and for practicing exploration geoscienti

This book takes readers on a multi-perspective tour through state-of-the-art mathematical developments related to the numerical treatment of PDEs based on splines, and in particular isogeometric metho

This textbook introduces step by step the basic numerical methods to solve the equations governing the motion of the atmosphere and ocean, and describes how to develop a set of corresponding instructi

Applied Numerical Methods with MATLAB is written for students who want to learn and apply numerical methods in order to solve problems in engineering and science. As such, the methods are motivated by

This contributed volume considers recent advances in dynamic games and their applications, based on presentations given at the 17th Symposium of the International Society of Dynamic Games, held July 1

This textbook offers an accessible introduction to the theory and numerics of approximation methods, combining classical topics of approximation with recent advances in mathematical signal processing,

The purpose of this book is to introduce and study numerical methods basic and advanced ones for scientific computing. This last refers to the implementation of appropriate approaches to t

This new edition of Numerical Ecology with R guides readers through an applied exploration of the major methods of multivariate data analysis, as seen through the eyes of three ecologists. It provides

This concise text introduces numerical analysis as a practical, problem-solving discipline. The three-part presentation begins with the fundamentals of functional analysis and approximation theory. Pa

This book combines a comprehensive state-of-the-art analysis of bifurcations of discrete-time dynamical systems with concrete instruction on implementations (and example applications) in the free MATLAB® software MatContM developed by the authors. While self-contained and suitable for independent study, the book is also written with users in mind and is an invaluable reference for practitioners. Part I focuses on theory, providing a systematic presentation of bifurcations of fixed points and cycles of finite-dimensional maps, up to and including cases with two control parameters. Several complementary methods, including Lyapunov exponents, invariant manifolds and homoclinic structures, and parts of chaos theory, are presented. Part II introduces MatContM through step-by-step tutorials on how to use the general numerical methods described in Part I for simple dynamical models defined by one- and two-dimensional maps. Further examples in Part III show how MatContM can be used to analyze

This hands-on introduction to numerical geodynamic modelling provides a solid grounding in the necessary mathematical theory and techniques, including continuum mechanics and partial differential equations, before introducing key numerical modelling methods and applications. Fully updated, this second edition includes four completely new chapters covering the most recent advances in modelling inertial processes, seismic cycles and fluid-solid interactions, and the development of adaptive mesh refinement algorithms. Many well-documented, state-of-the-art visco-elasto-plastic 2D models are presented, which allow robust modelling of key geodynamic processes. Requiring only minimal prerequisite mathematical training, and featuring over sixty practical exercises and ninety MATLAB® examples, this user-friendly resource encourages experimentation with geodynamic models. It is an ideal introduction for advanced courses and can be used as a self-study aid for graduates seeking to master geodyna

This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This third volume collects authoritative chapters

This textbook provides a self-contained introduction to numerical methods in probability with a focus on applications to finance.Topics covered include the Monte Carlo simulation (including simulation