This textbook for undergraduate mathematics, science, and engineering students introduces the theory and applications of discrete Fourier and wavelet transforms using elementary linear algebra, without assuming prior knowledge of signal processing or advanced analysis.It explains how to use the Fourier matrix to extract frequency information from a digital signal and how to use circulant matrices to emphasize selected frequency ranges. It introduces discrete wavelet transforms for digital signals through the lifting method and illustrates through examples and computer explorations how these transforms are used in signal and image processing. Then the general theory of discrete wavelet transforms is developed via the matrix algebra of two-channel filter banks. Finally, wavelet transforms for analog signals are constructed based on filter bank results already presented, and the mathematical framework of multiresolution analysis is examined.

Biometrics, the science of using physical traits to identify individuals, is playing an increasing role in our security-conscious society and across the globe. Biometric authentication, or bioauthentication, systems are being used to secure everything from amusement parks to bank accounts to military installations. Yet developments in this field have not been matched by an equivalent improvement in the statistical methods for evaluating these systems. Compensating for this need, this unique text/reference provides a basic statistical methodology for practitioners and testers of bioauthentication devices, supplying a set of rigorous statistical methods for evaluating biometric authentication systems. This framework of methods can be extended and generalized for a wide range of applications and tests. This is the first single resource on statistical methods for estimation and comparison of the performance of biometric authentication systems. The book focuses on six common performance metrics: for each metric, statistical methods are derived for a single system that incorporates confidence intervals, hypothesis tests, sample size calculations, power calculations and prediction intervals. These methods are also extended to allow for the statistical comparison and evaluation of multiple systems for both independent and paired data. Topics and features: * Provides a statistical methodology for the most common biometric performance metrics: failure to enroll (FTE), failure to acquire (FTA), false non-match rate (FNMR), false match rate (FMR), and receiver operating characteristic (ROC) curves * Presents methods for the comparison of two or more biometric performance metrics * Introduces a new bootstrap methodology for FMR and ROC curve estimation * Supplies more than 120 examples, using publicly available biometric data where possible * Discusses the addition of prediction intervals to the bioauthentication statistical toolset * Describes sample-size and power calculations for FTE, FTA, FNMR and FMR Researchers, managers and decisions makers needing to compare biometric systems across a variety of metrics will find within this reference an invaluable set of statistical tools. Written for an upper-level undergraduate or master's level audience with a quantitative background, readers are also expected to have an understanding of the topics in a typical undergraduate statistics course. Dr. Michael E. Schuckers is Associate Professor of Statistics at St. Lawrence University, Canton, NY, and a member of the Center for Identification Technology Research.

Digital Signal Processing in Power System Protection and Control bridges the gap between the theory of protection and control and the practical applications of protection equipment. Understanding how protection functions is crucial not only for equipment developers and manufacturers, but also for their users who need to install, set and operate the protection devices in an appropriate manner. After introductory chapters related to protection technology and functions, Digital Signal Processing in Power System Protection and Control presents the digital algorithms for signal filtering, followed by measurement algorithms of the most commonly-used protection criteria values and decision-making methods in protective relays. A large part of the book is devoted to the basic theory and applications of artificial intelligence techniques for protection and control. Fuzzy logic based schemes, artificial neural networks, expert systems and genetic algorithms with their advantages and drawbacks are discussed. AI techniques are compared and it is also shown how they can be combined to eliminate the disadvantages and magnify the useful features of particular techniques. The information provided in Digital Signal Processing in Power System Protection and Control can be useful for protection engineers working in utilities at various levels of the electricity network, as well as for students of electrical engineering, especially electrical power engineering. It may also be helpful for other readers who want to get acquainted with and to apply the filtering, measuring and decision-making algorithms for purposes other than protection and control, everywhere fast and on-line signal analysis is needed for proper functioning of the apparatus.

Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensible tool in science and technology. This textbook aims at providing a thorough introduction to the construction, analysis, and implementation of finite element methods for model problems arising in continuum mechanics. The first part of the book discusses elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods. The second part is devoted to the optimal adaptive approximation of singularities and the fast iterative solution of linear systems of equations arising from finite element discretizations. In the third part, the mathematical framework for analyzing and discretizing saddle-point problems is formulated, corresponding finte element methods are analyzed, and particular applications including incompressible elasticity, thin elastic objects, electromagnetism, and fluid mechanics are addressed. The book includes theoretical problems and practical projects for all chapters, and an introduction to the implementation of finite element methods.

Probably the first book to describe computational methods for numerically computing steady state and Hopf bifurcations. Requiring only a basic knowledge of calculus, and using detailed examples, problems, and figures, this is an ideal textbook for graduate students.

Matrix functions and matrix equations are widely used in science, engineering and social sciences due to the succinct and insightful way in which they allow problems to be formulated and solutions to be expressed. This book covers materials relevant to advanced undergraduate and graduate courses in numerical linear algebra and scientific computing. It is also well-suited for self-study. The broad content makes it convenient as a general reference to the subjects.

This book gathers twenty-two papers presented at the second NLAGA-BIRS Symposium, which was held at Cap Skirring and at the Assane Seck University in Ziguinchor, Senegal, on January 25-30, 2022. The five-day symposium brought together African experts on nonlinear analysis and geometry and their applications, as well as their international partners, to present and discuss mathematical results in various areas. The main goal of the NLAGA project is to advance and consolidate the development of these mathematical fields in West and Central Africa with a focus on solving real-world problems such as coastal erosion, pollution, and urban network and population dynamics problems. The book addresses a range of topics related to partial differential equations, geometric analysis, geometric structures, dynamics, optimization, inverse problems, complex analysis, algebra, algebraic geometry, control theory, stochastic approximations, and modelling.

This unique book provides a comprehensive introduction to computational mathematics, which forms an essential part of contemporary numerical algorithms, scientific computing and optimization. It uses a theorem-free approach with just the right balance between mathematics and numerical algorithms. This edition covers all major topics in computational mathematics with a wide range of carefully selected numerical algorithms, ranging from the root-finding algorithm, numerical integration, numerical methods of partial differential equations, finite element methods, optimization algorithms, stochastic models, nonlinear curve-fitting to data modelling, bio-inspired algorithms and swarm intelligence. This book is especially suitable for both undergraduates and graduates in computational mathematics, numerical algorithms, scientific computing, mathematical programming, artificial intelligence and engineering optimization. Thus, it can be used as a textbook and/or reference book.

This book covers an interdisciplinary approach for understanding mathematical modeling by offering a collection of models, solved problems related to the models, the methodologies employed, and the results using projects and case studies with insight into the operation of substantial real-time systems. The book covers a broad scope in the areas of statistical science, probability, stochastic processes, fluid dynamics, supply chain, optimization, and applications. It discusses advanced topics and the latest research findings, uses an interdisciplinary approach for real-time systems, offers a platform for integrated research, and identifies the gaps in the field for further research. The book is for researchers, students, and teachers that share a goal of learning advanced topics and the latest research in mathematical modeling.

This unique book provides a comprehensive introduction to computational mathematics, which forms an essential part of contemporary numerical algorithms, scientific computing and optimization. It uses a theorem-free approach with just the right balance between mathematics and numerical algorithms. This edition covers all major topics in computational mathematics with a wide range of carefully selected numerical algorithms, ranging from the root-finding algorithm, numerical integration, numerical methods of partial differential equations, finite element methods, optimization algorithms, stochastic models, nonlinear curve-fitting to data modelling, bio-inspired algorithms and swarm intelligence. This book is especially suitable for both undergraduates and graduates in computational mathematics, numerical algorithms, scientific computing, mathematical programming, artificial intelligence and engineering optimization. Thus, it can be used as a textbook and/or reference book.

Reduced order modeling is an important, growing field in computational science and engineering, and this is the first book to address the subject in relation to computational fluid dynamics. It focuses on complex parametrization of shapes for their optimization and includes recent developments in advanced topics such as turbulence, stability of flows, inverse problems, optimization, and flow control, as well as applications. This book will be of interest to researchers and graduate students in the field of reduced order modeling.

This book contains papers presented at the Workshop on the Analysis of Large-scale, High-Dimensional, and Multi-Variate Data Using Topology and Statistics, held in Le Barp, France, June 2013. It features the work of some of the most prominent and recognized leaders in the field who examine challenges as well as detail solutions to the analysis of extreme scale data. The book presents new methods that leverage the mutual strengths of both topological and statistical techniques to support the management, analysis, and visualization of complex data. It covers both theory and application and provides readers with an overview of important key concepts and the latest research trends. Coverage in the book includes multi-variate and/or high-dimensional analysis techniques, feature-based statistical methods, combinatorial algorithms, scalable statistics algorithms, scalar and vector field topology, and multi-scale representations. In addition, the book details algorithms that are broadly applicable and can be used by application scientists to glean insight from a wide range of complex data sets.

Knowledge management is far-reaching. It can dramatically reduce costs such as costs of office work repetition, human resource retirement, information reuse, etc. Rather than "reinventing the wheel" and having it be a costly and inefficient activity, systematic reuse of knowledge can show substantial cost benefits immediately. This book shows how to develop process-oriented methodologies, covers both interorganizational and enterprises models, discusses how knowledge management can dramatically reduce costs and increase speed of response, presents a wide range of quantitative methods applied to various knowledge engineering problems, and offers several graphical presentations of models and processes. Academicians and practitioners in the area of knowledge management and engineering, especially managers in industries will fine this book useful. The material might also be useful in knowledge management graduate studies.

This open access book demonstrates all the steps required to design heuristic algorithms for difficult optimization. The classic problem of the travelling salesman is used as a common thread to illustrate all the techniques discussed. This problem is ideal for introducing readers to the subject because it is very intuitive and its solutions can be graphically represented. The book features a wealth of illustrations that allow the concepts to be understood at a glance. The book approaches the main metaheuristics from a new angle, deconstructing them into a few key concepts presented in separate chapters: construction, improvement, decomposition, randomization and learning methods. Each metaheuristic can then be presented in simplified form as a combination of these concepts. This approach avoids giving the impression that metaheuristics is a non-formal discipline, a kind of cloud sculpture. Moreover, it provides concrete applications of the travelling salesman problem, which illustrate in just a few lines of code how to design a new heuristic and remove all ambiguities left by a general framework. Two chapters reviewing the basics of combinatorial optimization and complexity theory make the book self-contained. As such, even readers with a very limited background in the field will be able to follow all the content.

Computational Methods for Numerical Analysis with R is an overview of traditional numerical analysis topics presented using R. This guide shows how common functions from linear algebra, interpolation, numerical integration, optimization, and differential equations can be implemented in pure R code. Every algorithm described is given with a complete function implementation in R, along with examples to demonstrate the function and its use. Computational Methods for Numerical Analysis with R is intended for those who already know R, but are interested in learning more about how the underlying algorithms work. As such, it is suitable for statisticians, economists, and engineers, and others with a computational and numerical background.

This book develops a systematic and rigorous mathematical theory of finite difference methods for linear elliptic, parabolic and hyperbolic partial differential equations with nonsmooth solutions.
Finite difference methods are a classical class of techniques for the numerical approximation of partial differential equations. Traditionally, their convergence analysis presupposes the smoothness of the coefficients, source terms, initial and boundary data, and of the associated solution to the differential equation. This then enables the application of elementary analytical tools to explore their stability and accuracy. The assumptions on the smoothness of the data and of the associated analytical solution are however frequently unrealistic. There is a wealth of boundary - and initial - value problems, arising from various applications in physics and engineering, where the data and the corresponding solution exhibit lack of regularity.
In such instances classical techniques for the error analysis of finite difference schemes break down. The objective of this book is to develop the mathematical theory of finite difference schemes for linear partial differential equations with nonsmooth solutions.
"Analysis of Finite Difference Schemes" is aimed at researchers and graduate students interested in the mathematical theory of numerical methods for the approximate solution of partial differential equations.

Spotlighting the field of Multidisciplinary Design Optimization (MDO), this book illustrates and implements state-of-the-art methodologies within the complex process of aerospace system design under uncertainties. The book provides approaches to integrating a multitude of components and constraints with the ultimate goal of reducing design cycles. Insights on a vast assortment of problems are provided, including discipline modeling, sensitivity analysis, uncertainty propagation, reliability analysis, and global multidisciplinary optimization. The extensive range of topics covered include areas of current open research. This Work is destined to become a fundamental reference for aerospace systems engineers, researchers, as well as for practitioners and engineers working in areas of optimization and uncertainty. Part I is largely comprised of fundamentals. Part II presents methodologies for single discipline problems with a review of existing uncertainty propagation, reliability analysis, and optimization techniques. Part III is dedicated to the uncertainty-based MDO and related issues. Part IV deals with three MDO related issues: the multifidelity, the multi-objective optimization and the mixed continuous/discrete optimization and Part V is devoted to test cases for aerospace vehicle design.

Prolate Spheroidal Wave Functions (PSWFs) are the eigenfunctions of the bandlimited operator in one dimension. As such, they play an important role in signal processing, Fourier analysis, and approximation theory. While historically the numerical evaluation of PSWFs presented serious difficulties, the developments of the last fifteen years or so made them as computationally tractable as any other class of special functions. As a result, PSWFs have been becoming a popular computational tool. The present book serves as a complete, self-contained resource for both theory and computation. It will be of interest to a wide range of scientists and engineers, from mathematicians interested in PSWFs as an analytical tool to electrical engineers designing filters and antennas.

The topics faced in this book cover a large spectrum of current trends in mathematics, such as Shimura varieties and the Lang lands program, zonotopal combinatorics, non linear potential theory, variational methods in imaging, Riemann holonomy and algebraic geometry, mathematical problems arising in kinetic theory, Boltzmann systems, Pell's equations in polynomials, deformation theory in non commutative algebras. This work contains a selection of contributions written by international leading mathematicians who were speakers at the "INdAM Day", an initiative born in 2004 to present the most recent developments in contemporary mathematics.

The discussions and plans on all scienti?c, advisory, and political levels to realize an even larger "European Supercomputer" in Germany, where the hardware costs alone will be hundreds of millions Euro - much more than in the past - are getting closer to realization. As part of the strategy, the three national supercomputing centres HLRS (Stuttgart), NIC/JSC (Julic h) and LRZ (Munich) have formed the Gauss Centre for Supercomputing (GCS) as a new virtual organization enabled by an agreement between the Federal Ministry of Education and Research (BMBF) and the state ministries for research of Baden-Wurttem berg, Bayern, and Nordrhein-Westfalen. Already today, the GCS provides the most powerful high-performance computing - frastructure in Europe. Through GCS, HLRS participates in the European project PRACE (Partnership for Advances Computing in Europe) and - tends its reach to all European member countries. These activities aligns well with the activities of HLRS in the European HPC infrastructure project DEISA (Distributed European Infrastructure for Supercomputing Appli- tions) and in the European HPC support project HPC-Europa. Beyond that, HLRS and its partners in the GCS have agreed on a common strategy for the installation of the next generation of leading edge HPC hardware over the next ?ve years. The University of Stuttgart and the University of Karlsruhe have furth- more agreed to bundle their competences and resources.

This new work is an introduction to the numerical solution of the initial value problem for a system of ordinary differential equations. The first three chapters are general in nature, and chapters 4 through 8 derive the basic numerical methods, prove their convergence, study their stability and consider how to implement them effectively. The book focuses on the most important methods in practice and develops them fully, uses examples throughout, and emphasizes practical problem-solving methods.

Despite significant advances in technology and equipment for rolled steel, the computerization of production processes and the steady increase in production of sheet steel, recent scientific and technological achievements have not been compiled in the special literature and revealed to a wide range of specialists. This book details new approaches, computational techniques, and reliable calculation methods of leaf-rolling modes, forecasting and optimization of the technologies, increasing productivity of the mill and a radical improvement in the quality of steel products.

This book collects the final versions of the highest quality papers presented at the conference 11th European Symposium on Computational Intelligence and Mathematics held on October 2-5, 2019, in Toledo (Spain). The conjugation of computational sciences with different mathematical tools is essential in order to solve different challenges that arise in a wide-ranging knowledge areas. Nowadays, many promising research lines are being developed in this direction from the theoretical and applicational perspectives. In this publication, computational intelligence and mathematics are combined in interesting research works that aim to give answers to complex real problems. Moreover, the technical program of this conference included four excellent keynote speeches, given by Prof. Jose Luis Verdegay (Guidelines to solve Decision Making Problems), Prof. Joao Paulo Carvalho (Recommender Systems: Using Fuzzy Fingerprints for ``Proper'' Recommendations), Dr. Andreja Tepavcevic (Special lattice valued structures and approximate solutions of linear equations), and Prof. Juan Moreno-Garcia (Generating linguistic descriptions using Linguistic Petri Nets).

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 is composed of two parts: Mathematical and Numerical Analysis for Strongly Nonlinear Plasma Models and Exact Controllability and Observability for Quasilinear Hyperbolic Systems and Applications. It presents recent progress and results obtained in the domains related to both subjects without attaching much importance to the details of proofs but rather to difficulties encountered, to open problems and possible ways to be exploited. It will be very useful for promoting further study on some important problems in the future.