cambridge monographs on applied and computational

Spectral and Spectral Element Methods for Fractional Ordinary and Partial Differential Equations

作者：Mohsen Zayernouri (Michigan State University); Li-Lian (Nanyang Technological University Wang Singapore); Jie (Eastern Institute of Technology Shen Ningbo China); George Em (Brown University Karniadakis 出版社：Cambridge University Press 出版日：2024/09/30 裝訂：精裝

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2.

Quasi-Interpolation

作者：Martin Buhmann 出版社：Cambridge Univ Pr 出版日：2022/03/31 裝訂：精裝

Quasi-interpolation is one of the most useful and often applied methods for the approximation of functions and data in mathematics and applications. Its advantages are manifold: quasi-interpolants are able to approximate in any number of dimensions, they are efficient and relatively easy to formulate for scattered and meshed nodes and for any number of data. This book provides an introduction into the field for graduate students and researchers, outlining all the mathematical background and methods of implementation. The mathematical analysis of quasi-interpolation is given in three directions, namely on the basis (spline spaces, radial basis functions) from which the approximation is taken, on the form and computation of the quasi-interpolants (point evaluations, averages, least squares), and on the mathematical properties (existence, locality, convergence questions, precision). Learn which type of quasi-interpolation to use in different contexts and how to optimise its features to

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90折

3.

Schwarz-christoffel Mapping

作者：Tobin A. Driscoll 出版社：Cambridge Univ Pr 出版日：2002/08/01 裝訂：精裝

This book provides a comprehensive look at the Schwarz-Christoffel transformation, including its history and foundations, practical computation, common and less common variations, and many applications in fields such as electromagnetism, fluid flow, design and inverse problems, and the solution of linear systems of equations. It is an accessible resource for engineers, scientists, and applied mathematicians who seek more experience with theoretical or computational conformal mapping techniques. The most important theoretical results are stated and proved, but the emphasis throughout remains on concrete understanding and implementation, as evidenced by the 76 figures based on quantitatively correct illustrative examples. There are over 150 classical and modern reference works cited for readers needing more details. There is also a brief appendix illustrating the use of the Schwarz-Christoffel Toolbox for MATLAB, a package for computation of these maps.

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定價：3509 元，優惠價：9 3158

4.

Matrix Preconditioning Techniques And Applications

作者：Ke Chen 出版社：Cambridge Univ Pr 出版日：2005/07/25 裝訂：精裝

Preconditioning techniques have emerged as an essential part of successful and efficient iterative solutions of matrices. Ke Chen's book offers a comprehensive introduction to these methods. A vast range of explicit and implicit sparse preconditioners are covered, including the conjugate gradient, multi-level and fast multi-pole methods, matrix and operator splitting, fast Fourier and wavelet transforms, incomplete LU and domain decomposition, Schur complements and approximate inverses. In addition, aspects of parallel realization using the MPI are discussed. Very much a users-guide, the book provides insight to the use of these techniques in areas such as acoustic wave scattering, image restoration and bifurcation problems in electrical power stations. Supporting MATLAB files are available from the Web to support and develop readers' understanding, and provide stimulus for further study. Pitched at graduate level, the book is intended to serve as a useful guide and reference for

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5.

Multiscale Methods for Fredholm Integral Equations

作者：Zhongying Chen 出版社：Cambridge Univ Pr 出版日：2015/07/31 裝訂：精裝

The recent appearance of wavelets as a new computational tool in applied mathematics has given a new impetus to the field of numerical analysis of Fredholm integral equations. This book gives an account of the state of the art in the study of fast multiscale methods for solving these equations based on wavelets. The authors begin by introducing essential concepts and describing conventional numerical methods. They then develop fast algorithms and apply these to solving linear, nonlinear Fredholm integral equations of the second kind, ill-posed integral equations of the first kind and eigen-problems of compact integral operators. Theorems of functional analysis used throughout the book are summarised in the appendix. The book is an essential reference for practitioners wishing to use the new techniques. It may also be used as a text, with the first five chapters forming the basis of a one-semester course for advanced undergraduates or beginning graduates.

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6.

Partial Differential Equation Methods for Image Inpainting

作者：Carola-Bibiane Schönlieb 出版社：Cambridge Univ Pr 出版日：2015/10/31 裝訂：精裝

This book is concerned with digital image processing techniques that use partial differential equations (PDEs) for the task of image 'inpainting', an artistic term for virtual image restoration or interpolation, whereby missing or occluded parts in images are completed based on information provided by intact parts. Computer graphic designers, artists and photographers have long used manual inpainting to restore damaged paintings or manipulate photographs. Today, mathematicians apply powerful methods based on PDEs to automate this task. This book introduces the mathematical concept of PDEs for virtual image restoration. It gives the full picture, from the first modelling steps originating in Gestalt theory and arts restoration to the analysis of resulting PDE models, numerical realisation and real-world application. This broad approach also gives insight into functional analysis, variational calculus, optimisation and numerical analysis and will appeal to researchers and graduate

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7.

Volterra Integral Equations ─ An Introduction to Theory and Applications

作者：Hermann Brunner 出版社：Cambridge Univ Pr 出版日：2017/02/28 裝訂：精裝

This book offers a comprehensive introduction to the theory of linear and nonlinear Volterra integral equations (VIEs), ranging from Volterra's fundamental contributions and the resulting classical theory to more recent developments that include Volterra functional integral equations with various kinds of delays, VIEs with highly oscillatory kernels, and VIEs with non-compact operators. It will act as a 'stepping stone' to the literature on the advanced theory of VIEs, bringing the reader to the current state of the art in the theory. Each chapter contains a large number of exercises, extending from routine problems illustrating or complementing the theory to challenging open research problems. The increasingly important role of VIEs in the mathematical modelling of phenomena where memory effects play a key role is illustrated with some 30 concrete examples, and the notes at the end of each chapter feature complementary references as a guide to further reading.

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8.

Discrete Variational Problems with Interfaces

作者：Roberto Alicandro (Universita degli Studi di Napoli 'Federico II'); Andrea (Scuola Internazionale Superiore di Studi Avanzati Braides Trieste); Marco Cicalese (Technische Universitat Munchen); Margheri 出版社：Cambridge University Press 出版日：2024/01/31 裝訂：精裝

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The Christoffel-Darboux Kernel for Data Analysis

滿額折

9.

The Christoffel-Darboux Kernel for Data Analysis

作者：Jean Bernard Lasserre; Edouard Pauwels (Universite Paul Sabatier ); Mihai (University of California Putinar Santa Barbara) 出版社：Cambridge University Press 出版日：2022/04/30 裝訂：精裝

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定價：2469 元，優惠價：9 2222

10.

Geometry of the Phase Retrieval Problem：Graveyard of Algorithms

作者：Alexander H. Barnett 出版社：Cambridge Univ Pr 出版日：2022/04/30 裝訂：精裝

Recovering the phase of the Fourier transform is a ubiquitous problem in imaging applications from astronomy to nanoscale X-ray diffraction imaging. Despite the efforts of a multitude of scientists, from astronomers to mathematicians, there is, as yet, no satisfactory theoretical or algorithmic solution to this class of problems. Written for mathematicians, physicists and engineers working in image analysis and reconstruction, this book introduces a conceptual, geometric framework for the analysis of these problems, leading to a deeper understanding of the essential, algorithmically independent, difficulty of their solutions. Using this framework, the book studies standard algorithms and a range of theoretical issues in phase retrieval and provides several new algorithms and approaches to this problem with the potential to improve the reconstructed images. The book is lavishly illustrated with the results of numerous numerical experiments that motivate the theoretical development and

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11.

Symmetry, Phase Modulation and Nonlinear Waves

作者：Thomas J. Bridges 出版社：Cambridge Univ Pr 出版日：2017/07/31 裝訂：精裝

Nonlinear waves are pervasive in nature, but are often elusive when they are modelled and analysed. This book develops a natural approach to the problem based on phase modulation. It is both an elaboration of the use of phase modulation for the study of nonlinear waves and a compendium of background results in mathematics, such as Hamiltonian systems, symplectic geometry, conservation laws, Noether theory, Lagrangian field theory and analysis, all of which combine to generate the new theory of phase modulation. While the build-up of theory can be intensive, the resulting emergent partial differential equations are relatively simple. A key outcome of the theory is that the coefficients in the emergent modulation equations are universal and easy to calculate. This book gives several examples of the implications in the theory of fluid mechanics and points to a wide range of new applications.

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Difference Equations by Differential Equation Methods

90折

12.

Difference Equations by Differential Equation Methods

作者：Peter E. Hydon 出版社：Cambridge Univ Pr 出版日：2014/08/31 裝訂：精裝

Most well-known solution techniques for differential equations exploit symmetry in some form. Systematic methods have been developed for finding and using symmetries, first integrals and conservation laws of a given differential equation. Here the author explains how to extend these powerful methods to difference equations, greatly increasing the range of solvable problems. Beginning with an introduction to elementary solution methods, the book gives readers a clear explanation of exact techniques for ordinary and partial difference equations. The informal presentation is suitable for anyone who is familiar with standard differential equation methods. No prior knowledge of difference equations or symmetry is assumed. The author uses worked examples to help readers grasp new concepts easily. There are 120 exercises of varying difficulty and suggestions for further reading. The book goes to the cutting edge of research; its many new ideas and methods make it a valuable reference for

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定價：2469 元，優惠價：9 2222

13.

Spaces of Measures and their Applications to Structured Population Models

作者：Christian Düll 出版社：Cambridge Univ Pr 出版日：2021/10/31 裝訂：精裝

Structured population models are transport-type equations often applied to describe evolution of heterogeneous populations of biological cells, animals or humans, including phenomena such as crowd dynamics or pedestrian flows. This book introduces the mathematical underpinnings of these applications, providing a comprehensive analytical framework for structured population models in spaces of Radon measures. The unified approach allows for the study of transport processes on structures that are not vector spaces (such as traffic flow on graphs) and enables the analysis of the numerical algorithms used in applications. Presenting a coherent account of over a decade of research in the area, the text includes appendices outlining the necessary background material and discusses current trends in the theory, enabling graduate students to jump quickly into research.

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14.

Numerical Bifurcation Analysis of Maps ― From Theory to Software

作者：Yuri A. Kuznetsov 出版社：Cambridge Univ Pr 出版日：2019/05/31 裝訂：精裝

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

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15.

Mathematical Modelling of the Human Cardiovascular System ― Data, Numerical Approximation, Clinical Applications

作者：Alfio Quarteroni 出版社：Cambridge Univ Pr 出版日：2019/06/30 裝訂：精裝

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

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16.

Multivariate Approximation

作者：V. Temlyakov 出版社：Cambridge Univ Pr 出版日：2018/07/31 裝訂：精裝

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.

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17.

Operator-adapted Wavelets, Fast Solvers, and Numerical Homogenization ― From a Game Theoretic Approach to Numerical Approximation and Algorithm Design

作者：Houman Owhadi 出版社：Cambridge Univ Pr 出版日：2019/12/31 裝訂：精裝

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

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Spectral and Spectral Element Methods for Fractional Ordinary and Partial Differential Equations

Quasi-Interpolation

Schwarz-christoffel Mapping

Matrix Preconditioning Techniques And Applications

Multiscale Methods for Fredholm Integral Equations

Partial Differential Equation Methods for Image Inpainting

Volterra Integral Equations ─ An Introduction to Theory and Applications

Discrete Variational Problems with Interfaces

The Christoffel-Darboux Kernel for Data Analysis

Geometry of the Phase Retrieval Problem：Graveyard of Algorithms

Symmetry, Phase Modulation and Nonlinear Waves

Difference Equations by Differential Equation Methods

Spaces of Measures and their Applications to Structured Population Models

Numerical Bifurcation Analysis of Maps ― From Theory to Software

Mathematical Modelling of the Human Cardiovascular System ― Data, Numerical Approximation, Clinical Applications

Multivariate Approximation

Operator-adapted Wavelets, Fast Solvers, and Numerical Homogenization ― From a Game Theoretic Approach to Numerical Approximation and Algorithm Design