Bøger udgivet af Society for Industrial & Applied Mathematics,U.S.

Introduces the basics of matrix analysis and presents representative methods and their corresponding theories in matrix computations.

This self-contained textbook covers the fundamentals of two basic topics of linear functional analysis: locally convex spaces and harmonic analysis. Readers will find detailed introductions to topological vector spaces, distribution theory, weak topologies, Fourier transform, Hilbert transform, and Calderon-Zygmund singular integrals.

Discusses the fundamental computational methods used for image reconstruction in computed tomography (CT). Unique in its emphasis on the interplay of modeling, computing, and algorithm development, the book presents underlying mathematical models for motivating and deriving the basic principles of CT reconstruction methods.

Provides an overview of global sensitivity analysis methods and algorithms, including their theoretical basis and mathematical properties. Throughout, readers can practice applications using the accompanying R code.

Presents a hands-on approach to numerical continuation and bifurcation for nonlinear PDEs in 1D, 2D and 3D; provides a concise review of analytical background and numerical methods; explains the use of the free MATLAB package pde2path via examples with ready to use code; and contains demo codes that can be adapted to the reader's given problem.

Covers the fundamentals of closely related topics: linear systems (linear equations and least-squares) and linear programming (optimizing a linear function subject to linear constraints). For each problem class, stable and efficient numerical algorithms intended for a finite-precision environment are derived and analysed.

A comprehensive treatment of optimization problems involving uncertain parameters for which stochastic models are available.

Provides in-depth coverage of fundamental topics in numerical linear algebra, including how to solve dense and sparse linear systems, compute QR factorizations, compute the eigendecomposition of a matrix, and solve linear systems using iterative methods such as conjugate gradient.

Expositions of quantitative methods and algorithms for biological data tend to be scattered through the technical literature, often across different fields, and are thus awkward to assimilate. This book documents one example of this: the relationship between the cell biology idea of metabolic networks and the mathematical idea of polyhedral cones.

Presents a special solution of underdetermined linear systems where the number of nonzero entries in the solution is very small compared to the total number of entries. This is called sparse solution. As underdetermined linear systems can be very different, the authors explain how to compute a sparse solution by many approaches.

Provides a lively and accessible introduction to the numerical solution of stochastic differential equations with the aim of making this subject available to the widest possible readership. The book presents an outline of the underlying convergence and stability theory while avoiding technical details.

Presents the first survey of the Localized Orthogonal Decomposition (LOD) method, a pioneering approach for the numerical homogenization of partial differential equations with multiscale data beyond periodicity and scale separation.

Presents a unified treatment of the development of the classical moment problem from the late 19th century to the middle of the 20th century; important connections between the moment problem and branches of analysis; and a unified exposition of important classical results, which are difficult to read in the original journals.

Provides a solid mathematical basis for understanding popular data science algorithms for clustering and classification and shows that an in-depth understanding of the mathematics powering these algorithms gives insight into the underlying data. It presents a step-by-step derivation of these algorithms.

Focuses on Gaussian quadrature and the related Christoffel function. The book makes Gauss quadrature rules of any order easily accessible for a large variety of weight functions and for arbitrary precision. It also documents and illustrates known as well as original approximations for Gauss quadrature weights and Christoffel functions.

Data clustering is an unsupervised process that divides a set of objects into homogeneous groups. Since the publication of the first edition of this book, development in the area has exploded, especially in clustering algorithms for big data and open-source software for cluster analysis. This second edition reflects these new developments.

Combines nonlinear optimization, mathematical control theory, and numerical solution of ordinary differential/differential-algebraic equations to solve optimal control problems.

The location of an object can often be determined from indirect measurements using a process called estimation. This book explains the mathematical formulation of location-estimation problems and the statistical properties of these mathematical models.

Focuses on the identification and treatment of data anomalies, including examples that highlight different types of anomalies, their potential consequences if left undetected and untreated, and options for dealing with them.

Explores nonlinear observability. The book provides a modern theory of observability based on a new paradigm borrowed from theoretical physics and the mathematical foundation of that paradigm. In the case of observability, this framework takes into account the group of invariance that is inherent to the concept of observability.

Covers the fundamental ideas related to classical Riemann solutions, including their special structure and the types of waves that arise, as well as the ideas behind fast approximate solvers for the Riemann problem. The emphasis is on the general ideas, but each chapter delves into a particular application.

Algorithms are a dominant force in modern culture, and every indication is that they will become more pervasive, not less. The best algorithms are undergirded by beautiful mathematics. This text cuts across discipline boundaries to highlight some of the most famous and successful algorithms, and the principles behind them.

An original and modern treatment of approximation theory for students in applied mathematics. Includes exercises, illustrations and Matlab code.

Describes a novel mathematical framework for solving problems in two-dimensional, multiply connected regions. The framework is built on a central theoretical concept: the prime function, whose significance for the applied sciences, especially for solving problems in multiply connected domains, has been missed until recent work by the author.

This third edition of MATLAB Guide completely revises and updates the best-selling second edition and is more than 25 per cent longer. The book remains a lively, concise introduction to the most popular and important features of MATLAB and the Symbolic Math Toolbox.

Describes the state of the art of the mathematical theory and numerical analysis of imaging. The authors survey and provide a unified view of imaging techniques, provide the necessary mathematical background and common framework, and give a detailed analysis of the numerical algorithms.

Provides the reader with a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems. It also addresses specialized topics such as image reconstruction, parameter identification, total variation methods, nonnegativity constraints, and regularization parameter selection methods.

Describes new weighted approximation techniques, combining the computational advantages of B-splines and standard finite elements.

A comprehensive guide for the numerical solution of PDEs using C++ for students, engineers and researchers. Includes reader-friendly code.