This well-respected book introduces readers to the theory and application of modern numerical approximation techniques. Providing an accessible treatment that only requires a calculus prerequisite, the authors explain how, why, and when approximation techniques can be expected to work-and why, in some situations, they fail. A wealth of examples and exercises develop readers' intuition, and demonstrate the subject's practical applications to important everyday problems in math, computing, engineering, and physical science disciplines. Three decades after it was first published, Burden, Faires, and Burden's NUMERICAL ANALYSIS remains the definitive introduction to a vital and practical subject.

Aiming to provide the reader with a general overview of the mathematical and numerical techniques used for the simulation of matter at the microscopic scale, this book lays the emphasis on the numerics, but modelling aspects are also addressed. The contributors come from different scientific communities: physics, theoretical chemistry, mathematical analysis, stochastic analysis, numerical analysis, and the text should be suitable for graduate students in mathematics, sciences and engineering and technology.

These volumes cover all the major aspects of numerical analysis. This particular volume discusses the solution of equations in Rn, Gaussian elimination, techniques of scientific computer, the analysis of multigrid methods, wavelet methods, and finite volume methods.

This series of volumes aims to cover the major aspects of Numerical Analysis, serving as the basic reference work on the subject. Each volume concentrates on one, two, or three, particular topics. Each article, is an in-depth survey, reflecting the most recent trends in the field, and is essentially self-contained. The handbook covers the basic methods of numerical analysis, under the following general headings: solution of equations in R n; finite difference methods; finite element methods; techniques of scientific computing; and optimization theory and systems science. It also covers the numerical solution of actual problems of contemporary interest in Applied Mathematics.

This series of volumes aims to cover all the major aspects of numerical analysis, serving as the basic reference work on the subject. Each volume will concentrate on one, two or three particular topics. Each article, written by an expert, is an in-depth survey, reflecting the most recent trends in the field, and is essentially self-contained. The Handbook will cover the basic methods of numerical analysis, under the following general headings: solution of equations in Rn; finite difference methods; finite element methods; techniques of scientific computing; and optimization theory and systems science. It will also cover the numerical solution of actual problems of contemporary interest in applied mathematics, under the following headings: numerical methods of fluids; numerical methods for solids; and specific applications - including meteorology, seismology, petroleum mechanics and celestial mechanics.

This book focuses on broadly defined areas of chemical information science- with special emphasis on chemical informatics- and computer-aided molecular design. The computational and cheminformatics methods discussed, and their application to drug discovery, are essential for sustaining a viable drug development pipeline. It is increasingly challenging to identify new chemical entities and the amount of money and time invested in research to develop a new drug has greatly increased over the past 50 years. The average time to take a drug from clinical testing to approval is currently 7.2 years. Therefore, the need to develop predictive computational techniques to drive research more efficiently to identify compounds and molecules, which have the greatest likelihood of being developed into successful drugs for a target, is of great significance. New methods such as high throughput screening (HTS) and techniques for the computational analysis of hits have contributed to improvements in drug discovery efficiency. The SARMs developed by Jurgen and colleagues have enabled display of SAR data in a more transparent scaffold/functional SAR table. There are many tools and databases available for use in applied drug discovery techniques based on polypharmacology. The cheminformatics approaches and methodologies presented in this volume and at the Skolnik Award Symposium will pave the way for improved efficiency in drug discovery. The lectures and the chapters also reflect the various aspects of scientific enquiry and research interests of the 2015 Herman Skolnik award recipient.

The subject of geomathematics focuses on the interpretation and classification of data from geoscientific and satellite sources, reducing information to a comprehensible form and allowing the testing of concepts. Sphere oriented mathematics plays an important part in this study and this book provides the necessary foundation for graduate students and researchers interested in any of the diverse topics of constructive approximation in this area. This book bridges the existing gap between monographs on special functions of mathematical physics and constructive approximation in Euclidean spaces. The primary objective is to provide readers with an understanding of aspects of approximation by spherical harmonics, such as spherical splines and wavelets, as well as indicating future directions of research. Scalar, vectorial, and tensorial methods are each considered in turn. The concentration on spherical splines and wavelets allows a double simplification; not only is the number of independent variables reduced resulting in a lower dimensional problem, but also radial basis function techniques become applicable. When applied to geomathematics this leads to new structures and methods by which sophisticated measurements and observations can be handled more efficiently, thus reducing time and costs.

This two volume work presents research workers and graduate students in numerical analysis with a state-of-the-art survey of some of the most active areas of numerical analysis. The work arises from a Summer School covering recent trends in the subject. The chapters are written by the main lecturers at the School each of whom are internationally renowned experts in their respective fields. This extensive coverage of the major areas of research will be invaluable for both theoreticians and practitioners. This volume covers research in the numerical analysis of nonlinear phenomena: evolution equations, free boundary problems, spectral methods, and numerical methods for dynamical systems, nonlinear stability, and differential equations on manifolds.

This volume collects numerous recent advances in the study of stratified fluids. It includes analytical and experimental work from a wide range of fields, including meteorology, limnology, oceanography, and the study of estuarine processes. It also includes fundamental research on stratified and rotating fluid dynamics. A compendium of current work, the book is an ideal starting point for future research.

Besides their intrinsic mathematical interest, geometric partial differential equations (PDEs) are ubiquitous in many scientific, engineering and industrial applications. They represent an intellectual challenge and have received a great deal of attention recently. The purpose of this volume is to provide a missing reference consisting of self-contained and comprehensive presentations. It includes basic ideas, analysis and applications of state-of-the-art fundamental algorithms for the approximation of geometric PDEs together with their impacts in a variety of fields within mathematics, science, and engineering.

Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 2, Volume 20, surveys the contemporary developments relating to the analysis and learning of images, shapes and forms, covering mathematical models and quick computational techniques. Chapter cover Alternating Diffusion: A Geometric Approach for Sensor Fusion, Generating Structured TV-based Priors and Associated Primal-dual Methods, Graph-based Optimization Approaches for Machine Learning, Uncertainty Quantification and Networks, Extrinsic Shape Analysis from Boundary Representations, Efficient Numerical Methods for Gradient Flows and Phase-field Models, Recent Advances in Denoising of Manifold-Valued Images, Optimal Registration of Images, Surfaces and Shapes, and much more.

Processing, Analyzing and Learning of Images, Shapes, and Forms: Volume 19, Part One provides a comprehensive survey of the contemporary developments related to the analysis and learning of images, shapes and forms. It covers mathematical models as well as fast computational techniques, and includes new chapters on Alternating diffusion: a geometric approach for sensor fusion, Shape Correspondence and Functional Maps, Geometric models for perception-based image processing, Decomposition schemes for nonconvex composite minimization: theory and applications, Low rank matrix recovery: algorithms and theory, Geometry and learning for deformation shape correspondence, and Factoring scene layout from monocular images in presence of occlusion.

The book aims at giving a monographic presentation of the abstract harmonic analysis of hypergroups, while combining it with applied topics of spectral analysis, approximation by orthogonal expansions and stochastic sequences. Hypergroups are locally compact Hausdorff spaces equipped with a convolution, an involution and a unit element. Related algebraic structures had already been studied by Frobenius around 1900. Their axiomatic characterisation in harmonic analysis was later developed in the 1970s. Hypergoups naturally emerge in seemingly different application areas as time series analysis, probability theory and theoretical physics.The book presents harmonic analysis on commutative and polynomial hypergroups as well as weakly stationary random fields and sequences thereon. For polynomial hypergroups also difference equations and stationary sequences are considered. At greater extent than in the existing literature, the book compiles a rather comprehensive list of hypergroups, in particular of polynomial hypergroups. With an eye on readers at advanced undergraduate and graduate level, the proofs are generally worked out in careful detail. The bibliography is extensive.

This book is the second edition of the first complete study and monograph dedicated to singular traces. The text offers, due to the contributions of Albrecht Pietsch and Nigel Kalton, a complete theory of traces and their spectral properties on ideals of compact operators on a separable Hilbert space. The second edition has been updated on the fundamental approach provided by Albrecht Pietsch. For mathematical physicists and other users of Connes' noncommutative geometry the text offers a complete reference to traces on weak trace class operators, including Dixmier traces and associated formulas involving residues of spectral zeta functions and asymptotics of partition functions.

This book is a description of why and how to do Scientific Computing for fundamental models of fluid flow. It contains introduction, motivation, analysis, and algorithms and is closely tied to freely available MATLAB codes that implement the methods described. The focus is on finite element approximation methods and fast iterative solution methods for the consequent linear(ized) systems arising in important problems that model incompressible fluid flow. The problems addressed are the Poisson equation, Convection-Diffusion problem, Stokes problem and Navier-Stokes problem, including new material on time-dependent problems and models of multi-physics. The corresponding iterative algebra based on preconditioned Krylov subspace and multigrid techniques is for symmetric and positive definite, nonsymmetric positive definite, symmetric indefinite and nonsymmetric indefinite matrix systems respectively. For each problem and associated solvers there is a description of how to compute together with theoretical analysis that guides the choice of approaches and describes what happens in practice in the many illustrative numerical results throughout the book (computed with the freely downloadable IFISS software). All of the numerical results should be reproducible by readers who have access to MATLAB and there is considerable scope for experimentation in the "computational laboratory " provided by the software. Developments in the field since the first edition was published have been represented in three new chapters covering optimization with PDE constraints (Chapter 5); solution of unsteady Navier-Stokes equations (Chapter 10); solution of models of buoyancy-driven flow (Chapter 11). Each chapter has many theoretical problems and practical computer exercises that involve the use of the IFISS software. This book is suitable as an introduction to iterative linear solvers or more generally as a model of Scientific Computing at an advanced undergraduate or beginning graduate level.

Acta Numerica is an annual publication containing invited survey papers by leading researchers in numerical mathematics and scientific computing. The papers present overviews of recent developments in their area and provide 'state of the art' techniques and analysis. This volume was originally published in 2010.

This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.

In this book, differential evolution and its modified variants are applied to the clustering of data and images. Metaheuristics have emerged as potential algorithms for dealing with complex optimization problems, which are otherwise difficult to solve using traditional methods. In this regard, differential evolution is considered to be a highly promising technique for optimization and is being used to solve various real-time problems. The book studies the algorithms in detail, tests them on a range of test images, and carefully analyzes their performance. Accordingly, it offers a valuable reference guide for all researchers, students and practitioners working in the fields of artificial intelligence, optimization and data analytics.

This book presents a novel approach to umbral calculus, which uses only elementary linear algebra (matrix calculus) based on the observation that there is an isomorphism between Sheffer polynomials and Riordan matrices, and that Sheffer polynomials can be expressed in terms of determinants. Additionally, applications to linear interpolation and operator approximation theory are presented in many settings related to various families of polynomials.

This book is considered the first extended survey on algorithms and techniques for efficient cohesive subgraph computation. With rapid development of information technology, huge volumes of graph data are accumulated. An availability of rich graph data not only brings great opportunities for realizing big values of data to serve key applications, but also brings great challenges in computation. Using a consistent terminology, the book gives an excellent introduction to the models and algorithms for the problem of cohesive subgraph computation. The materials of this book are well organized from introductory content to more advanced topics while also providing well-designed source codes for most algorithms described in the book. This is a timely book for researchers who are interested in this topic and efficient data structure design for large sparse graph processing. It is also a guideline book for new researchers to get to know the area of cohesive subgraph computation.

This book focuses on theoretical aspects of dynamical systems in the broadest sense. It highlights novel and relevant results on mathematical and numerical problems that can be found in the fields of applied mathematics, physics, mechanics, engineering and the life sciences. The book consists of contributed research chapters addressing a diverse range of problems. The issues discussed include (among others): numerical-analytical algorithms for nonlinear optimal control problems on a large time interval; gravity waves in a reservoir with an uneven bottom; value distribution and growth of solutions for certain Painleve equations; optimal control of hybrid systems with sliding modes; a mathematical model of the two types of atrioventricular nodal reentrant tachycardia; non-conservative instability of cantilevered nanotubes using the Cell Discretization Method; dynamic analysis of a compliant tensegrity structure for use in a gripper application; and Jeffcott rotor bifurcation behavior using various models of hydrodynamic bearings.