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Approximation and Online Algorithms: 4th International Workshop, Waoa 2006, Zurich, Switzerland, September 14-15, 2006, Revised Papers (Lecture Notes In Computer Science Ser. #4368)
by Christos Kaklamanis Asaf LevinThis book constitutes the thoroughly refereed workshop post-proceedings of the 18th International Workshop on Approximation and Online Algorithms, WAOA 2019, held virtually in September 2020 as part of ALGO 2020. <P><P> The 15 revised full papers presented this book were carefully reviewed and selected from 40 submissions. Topics of interest for WAOA 2018 were graph algorithms, inapproximability results, network design, packing and covering, paradigms for the design and analysis of approximation and online algorithms, parameterized complexity, scheduling problems, algorithmic game theory, algorithmic trading, coloring and partitioning, competitive analysis, computational advertising, computational -finance, cuts and connectivity, geometric problems, mechanism design, resource augmentation, real-world applications. Chapter "Explorable Uncertainty in Scheduling with Non-Uniform Testing Times" is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Approximation and Online Algorithms: 13th International Workshop, WAOA 2015, Patras, Greece, September 17-18, 2015. Revised Selected Papers (Lecture Notes in Computer Science #9499)
by Martin Skutella Laura SanitàThis book constitutes the thoroughly refereed post-workshop proceedings of the 13th International Workshop on Approximation and Online Algorithms, WAOA 2015, held in Patras, Greece, in September 2015 as part of ALGO 2015. The 17 revised full papers presented were carefully reviewed and selected from 40 submissions. Topics of interest for WAOA 2015 were: algorithmic game theory, algorithmic trading, coloring and partitioning, competitive analysis, computational advertising, computational finance, cuts and connectivity, geometric problems, graph algorithms, inapproximability, mechanism design, natural algorithms, network design, packing and covering, paradigms for the design and analysis of approximation and online algorithms, parameterized complexity, scheduling problems,and real-world applications.
Approximation and Optimization: Algorithms, Complexity and Applications (Springer Optimization and Its Applications #145)
by Ioannis C. Demetriou Panos M. PardalosThis book focuses on the development of approximation-related algorithms and their relevant applications. Individual contributions are written by leading experts and reflect emerging directions and connections in data approximation and optimization. Chapters discuss state of the art topics with highly relevant applications throughout science, engineering, technology and social sciences. Academics, researchers, data science practitioners, business analysts, social sciences investigators and graduate students will find the number of illustrations, applications, and examples provided useful. This volume is based on the conference Approximation and Optimization: Algorithms, Complexity, and Applications, which was held in the National and Kapodistrian University of Athens, Greece, June 29–30, 2017. The mix of survey and research content includes topics in approximations to discrete noisy data; binary sequences; design of networks and energy systems; fuzzy control; large scale optimization; noisy data; data-dependent approximation; networked control systems; machine learning ; optimal design; no free lunch theorem; non-linearly constrained optimization; spectroscopy.
Approximation by Max-Product Type Operators
by Sorin G. Gal Barnabás Bede Lucian CoroianuThis monograph presents a broad treatment of developments in an area of constructive approximation involving the so-called "max-product" type operators. The exposition highlights the max-product operators as those which allow one to obtain, in many cases, more valuable estimates than those obtained by classical approaches. The text considers a wide variety of operators which are studied for a number of interesting problems such as quantitative estimates, convergence, saturation results, localization, to name several. Additionally, the book discusses the perfect analogies between the probabilistic approaches of the classical Bernstein type operators and of the classical convolution operators (non-periodic and periodic cases), and the possibilistic approaches of the max-product variants of these operators. These approaches allow for two natural interpretations of the max-product Bernstein type operators and convolution type operators: firstly, as possibilistic expectations of some fuzzy variables, and secondly, as bases for the Feller type scheme in terms of the possibilistic integral. These approaches also offer new proofs for the uniform convergence based on a Chebyshev type inequality in the theory of possibility. Researchers in the fields of approximation of functions, signal theory, approximation of fuzzy numbers, image processing, and numerical analysis will find this book most beneficial. This book is also a good reference for graduates and postgraduates taking courses in approximation theory.
Approximation by Multivariate Singular Integrals (SpringerBriefs in Mathematics)
by George A. AnastassiouApproximation by Multivariate Singular Integrals is the first monograph to illustrate the approximation of multivariate singular integrals to the identity-unit operator. The basic approximation properties of the general multivariate singular integral operators is presented quantitatively, particularly special cases such as the multivariate Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular integral operators are examined thoroughly. This book studies the rate of convergence of these operators to the unit operator as well as the related simultaneous approximation. The last chapter, which includes many examples, presents a related Korovkin type approximation theorem for functions of two variables. Relevant background information and motivation is included in this exposition, and as a result this book can be used as supplementary text for several advanced courses. The results presented apply to many areas of pure and applied mathematics, such a mathematical analysis, probability, statistics and partial differential equations. This book is appropriate for researchers and selected seminars at the graduate level.
Approximation Methods for Polynomial Optimization: Models, Algorithms, and Applications (SpringerBriefs in Optimization)
by Zhening Li Simai He Shuzhong ZhangPolynomial optimization have been a hot research topic for the past few years and its applications range from Operations Research, biomedical engineering, investment science, to quantum mechanics, linear algebra, and signal processing, among many others. In this brief the authors discuss some important subclasses of polynomial optimization models arising from various applications, with a focus on approximations algorithms with guaranteed worst case performance analysis. The brief presents a clear view of the basic ideas underlying the design of such algorithms and the benefits are highlighted by illustrative examples showing the possible applications. This timely treatise will appeal to researchers and graduate students in the fields of optimization, computational mathematics, Operations Research, industrial engineering, and computer science.
Approximation Methods in Probability Theory (Universitext)
by Vydas ČekanavičiusThis book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems. While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.
Approximation Methods in Science and Engineering
by Reza N. JazarApproximation Methods in Engineering and Science covers fundamental and advanced topics in three areas: Dimensional Analysis, Continued Fractions, and Stability Analysis of the Mathieu Differential Equation. Throughout the book, a strong emphasis is given to concepts and methods used in everyday calculations. Dimensional analysis is a crucial need for every engineer and scientist to be able to do experiments on scaled models and use the results in real world applications. Knowing that most nonlinear equations have no analytic solution, the power series solution is assumed to be the first approach to derive an approximate solution. However, this book will show the advantages of continued fractions and provides a systematic method to develop better approximate solutions in continued fractions. It also shows the importance of determining stability chart of the Mathieu equation and reviews and compares several approximate methods for that. The book provides the energy-rate method to study the stability of parametric differential equations that generates much better approximate solutions.
Approximation of Euclidean Metric by Digital Distances
by Jayanta MukhopadhyayThis book discusses different types of distance functions defined in an n-D integral space for their usefulness in approximating the Euclidean metric. It discusses the properties of these distance functions and presents various kinds of error analysis in approximating Euclidean metrics. It also presents a historical perspective on efforts and motivation for approximating Euclidean metrics by digital distances from the mid-sixties of the previous century. The book also contains an in-depth presentation of recent progress, and new research problems in this area.
Approximation of Stochastic Invariant Manifolds: Stochastic Manifolds for Nonlinear SPDEs I (SpringerBriefs in Mathematics)
by Mickaël D. Chekroun Honghu Liu Shouhong WangThis first volume is concerned with the analytic derivation of explicit formulas for the leading-order Taylor approximations of (local) stochastic invariant manifolds associated with a broad class of nonlinear stochastic partial differential equations. These approximations take the form of Lyapunov-Perron integrals, which are further characterized in Volume II as pullback limits associated with some partially coupled backward-forward systems. This pullback characterization provides a useful interpretation of the corresponding approximating manifolds and leads to a simple framework that unifies some other approximation approaches in the literature. A self-contained survey is also included on the existence and attraction of one-parameter families of stochastic invariant manifolds, from the point of view of the theory of random dynamical systems.
Approximation-solvability of Nonlinear Functional and Differential Equations (Chapman And Hall/crc Pure And Applied Mathematics Ser. #171)
by Wolodymyr V. PetryshynThis reference/text develops a constructive theory of solvability on linear and nonlinear abstract and differential equations - involving A-proper operator equations in separable Banach spaces, and treats the problem of existence of a solution for equations involving pseudo-A-proper and weakly-A-proper mappings, and illustrates their applications.;Facilitating the understanding of the solvability of equations in infinite dimensional Banach space through finite dimensional appoximations, this book: offers an elementary introductions to the general theory of A-proper and pseudo-A-proper maps; develops the linear theory of A-proper maps; furnishes the best possible results for linear equations; establishes the existence of fixed points and eigenvalues for P-gamma-compact maps, including classical results; provides surjectivity theorems for pseudo-A-proper and weakly-A-proper mappings that unify and extend earlier results on monotone and accretive mappings; shows how Friedrichs' linear extension theory can be generalized to the extensions of densely defined nonlinear operators in a Hilbert space; presents the generalized topological degree theory for A-proper mappings; and applies abstract results to boundary value problems and to bifurcation and asymptotic bifurcation problems.;There are also over 900 display equations, and an appendix that contains basic theorems from real function theory and measure/integration theory.
Approximation Techniques for Engineers: Second Edition
by Louis KomzsikThis second edition includes eleven new sections based on the approximation of matrix functions, deflating the solution space and improving the accuracy of approximate solutions, iterative solution of initial value problems of systems of ordinary differential equations, and the method of trial functions for boundary value problems. The topics of th
Approximation Theory: In Memory of A.K. Varma (Chapman And Hall/crc Pure And Applied Mathematics Ser. #212)
by N. K. Govil R. N. Mahapatra Z. Nashed A. Sharma J. Szabados"Contains the contributions of 45 internationally distinguished mathematicians covering all areas of approximation theory-written in honor of the pioneering work of Arun K. Varma to the fields of interpolation and approximation of functions, including Birhoff interpolation and approximation by spline functions."
Approximation Theory and Analytic Inequalities
by Themistocles M. RassiasThis contributed volume focuses on various important areas of mathematics in which approximation methods play an essential role. It features cutting-edge research on a wide spectrum of analytic inequalities with emphasis on differential and integral inequalities in the spirit of functional analysis, operator theory, nonlinear analysis, variational calculus, featuring a plethora of applications, making this work a valuable resource. The reader will be exposed to convexity theory, polynomial inequalities, extremal problems, prediction theory, fixed point theory for operators, PDEs, fractional integral inequalities, multidimensional numerical integration, Gauss–Jacobi and Hermite–Hadamard type inequalities, Hilbert-type inequalities, and Ulam’s stability of functional equations. Contributions have been written by eminent researchers, providing up-to-date information and several results which may be useful to a wide readership including graduate students and researchers working in mathematics, physics, economics, operational research, and their interconnections.
Approximation Theory and Harmonic Analysis on Spheres and Balls (Springer Monographs in Mathematics)
by Feng Dai Yuan XuThis monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book contains mainstream material on the subject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes. The last part of the book features several applications, including cubature formulas, distribution of points on the sphere, and the reconstruction algorithm in computerized tomography. This book is directed at researchers and advanced graduate students in analysis. Mathematicians who are familiar with Fourier analysis and harmonic analysis will understand many of the concepts that appear in this manuscript: spherical harmonics, the Hardy-Littlewood maximal function, the Marcinkiewicz multiplier theorem, the Riesz transform, and doubling weights are all familiar tools to researchers in this area.
Approximation Theory and Numerical Analysis Meet Algebra, Geometry, Topology (Springer INdAM Series #60)
by Martina Lanini Carla Manni Henry SchenckThe book, based on the INdAM Workshop "Approximation Theory and Numerical Analysis Meet Algebra, Geometry, Topology" provides a bridge between different communities of mathematicians who utilize splines in their work. Splines are mathematical objects which allow researchers in geometric modeling and approximation theory to tackle a wide variety of questions. Splines are interesting for both applied mathematicians, and also for those working in purely theoretical mathematical settings. This book contains contributions by researchers from different mathematical communities: on the applied side, those working in numerical analysis and approximation theory, and on the theoretical side, those working in GKM theory, equivariant cohomology and homological algebra.
Approximation Theory XIV: San Antonio 2013 (Springer Proceedings in Mathematics & Statistics #83)
by Gregory E. Fasshauer Larry L. SchumakerThese proceedings were prepared in connection with the 14th International Conference on Approximation Theory, which was held April 7-10, 2013 in San Antonio, Texas. The conference was the fourteenth in a series of meetings in Approximation Theory held at various locations in the United States. The included invited and contributed papers cover diverse areas of approximation theory with a special emphasis on the most current and active areas such as compressed sensing, isogeometric analysis, anisotropic spaces, radial basis functions and splines. Classical and abstract approximation is also included The book will be of interest to mathematicians, engineers\ and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis and related application areas.
Approximation Theory XV: San Antonio 2016 (Springer Proceedings in Mathematics & Statistics #201)
by Gregory E. Fasshauer Larry L. SchumakerThese proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22-25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type. The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, approximation of fractional differential equations, numerical integration formulas, and trigonometric polynomial approximation.
Approximation Theory XVI: Nashville, TN, USA, May 19-22, 2019 (Springer Proceedings in Mathematics & Statistics #336)
by Gregory E. Fasshauer Marian Neamtu Larry L. SchumakerThese proceedings are based on the international conference Approximation Theory XVI held on May 19–22, 2019 in Nashville, Tennessee. The conference was the sixteenth in a series of meetings in Approximation Theory held at various locations in the United States. Over 130 mathematicians from 20 countries attended. The book contains two longer survey papers on nonstationary subdivision and Prony’s method, along with 11 research papers on a variety of topics in approximation theory, including Balian-Low theorems, butterfly spline interpolation, cubature rules, Hankel and Toeplitz matrices, phase retrieval, positive definite kernels, quasi-interpolation operators, stochastic collocation, the gradient conjecture, time-variant systems, and trivariate finite elements. The book should be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.
Approximation und Nichtlineare Optimierung in Praxisaufgaben: Anwendungen aus dem Finanzbereich und der Standortplanung (Studienbücher Wirtschaftsmathematik)
by Christiane Tammer Alfred Göpfert Thomas RiedrichIn diesem Buch wird die Vielgestaltigkeit von Optimierung und Approximation zusammen mit ihrem breiten Umfeld anhand von Aufgaben samt ihren L#65533;sungen und interpretierenden Aussagen zum Ausdruck gebracht. Fachlich steht dabei im Vordergrund, Methoden der Angewandten Analysis zu nutzen, um die Struktur und Eigenschaften der Probleme zu erkennen und handhabbare Optimalit#65533;tbedingungen herzuleiten, die die Behandlung der Aufgaben erm#65533;glichen und vereinfachen. Viele praktische Aufgabenstellungen f#65533;hren auf konvexe bzw. nichtkonvexe Optimierungsprobleme, Mehrkriterielle Optimierungsprobleme, Standortprobleme, Probleme der Risikotheorie, Versicherungsmathematik, Robuste Probleme und Signaltheorie, die in den vorgestellten Aufgaben diskutiert werden. Hinweise auf online-verf#65533;gbare Software werden gegeben. Das Buch richtet sich an Studierende der Wirtschaftsmathematik im Masterstudium.
Approximation with Positive Linear Operators and Linear Combinations (Developments in Mathematics #50)
by Vijay Gupta Gancho TachevThis book presents a systematic overview of approximation by linear combinations of positive linear operators, a useful tool used to increase the order of approximation. Fundamental and recent results from the past decade are described with their corresponding proofs. The volume consists of eight chapters that provide detailed insight into the representation of monomials of the operators Ln , direct and inverse estimates for a broad class of positive linear operators, and case studies involving finite and unbounded intervals of real and complex functions. Strong converse inequalities of Type A in terminology of Ditzian-Ivanov for linear combinations of Bernstein and Bernstein-Kantorovich operators and various Voronovskaja-type estimates for some linear combinations are analyzed and explained. Graduate students and researchers in approximation theory will find the list of open problems in approximation of linear combinations useful. The book serves as a reference for graduate and postgraduate courses as well as a basis for future study and development.
Approximation with Quasi-Splines
by G.H KirovIn the theory of splines, a function is approximated piece-wise by (usually cubic) polynomials. Quasi-splines is the natural extension of this, allowing us to use any useful class of functions adapted to the problem.Approximation with Quasi-Splines is a detailed account of this highly useful technique in numerical analysis.The book presents the requisite approximation theorems and optimization methods, developing a unified theory of one and several variables. The author applies his techniques to the evaluation of definite integrals (quadrature) and its many-variables generalization, which he calls "cubature."This book should be required reading for all practitioners of the methods of approximation, including researchers, teachers, and students in applied, numerical and computational mathematics.
AQA A Level Further Mathematics Discrete
by Nick GeereExam board: AQALevel: A-levelSubject: MathematicsFirst teaching: September 2017First exams: Summer 2019Whiteboard eTextbooks are online, interactive versions of the printed textbooks that are ideal for front-of-class teaching and lesson planning. The Whiteboard eTextbooks link seamlessly with MEI Integral Further Mathematics online resources, allowing you to move with ease between corresponding topics in the eTextbooks and Integral.Integral has been developed by MEI and supports teachers and students with high quality teaching and learning activities, including dynamic resources and self-marking tests and assessments that cover the new specifications.To have full access to the eTextbooks and Integral resources you must be subscribed to both Dynamic Learning and Integral. To subscribe to Integral, visit www.integralmaths.org. For more information on our eTextbooks and Integral please see the Quick Links box.Provide full support for the AQA Discrete content of the new specification with worked examples, stimulating activities and assessment support to help develop understanding, reasoning and problem solving. - Help prepare students for assessment with skills-building activities and fully worked examples and solutions tailored to the changed criteria.- Build understanding through carefully worded expositions that set out the basics and the detail of each topic, with call-outs to add clarity.- Test knowledge and develop understanding, reasoning and problem solving with banded Exercise questions that increase in difficulty (answers provided in the back of the book and online). - Gain a full understanding of the logical steps that are used in creating each individual algorithm - Encourages students to track their progress using learning outcomes and Key Points listed at the end of each chapter.
AQA A Level Further Mathematics Mechanics
by Jean-Paul MuscatAchieve your full potential with learning materials that guide you through the Mechanics content of the new AS and A-level specifications; developed by subject experts and authors sourced from MEI.- Develop reasoning and problem-solving skills with practice questions and differentiated exercises that improve mathematical techniques.- Overcome misconceptions and develop insight into problem-solving with annotated worked examples.- Build connections between topics with points of interest and links to real-world examples.- Consolidate understanding with end-of-chapter summaries of the key points.
AQA A Level Further Mathematics Statistics
by John du FeuBuild your knowledge and understanding with guidance and assessment preparation covering the Statistics options of the new AS and A-level specifications, from a team of subject experts and authors sourced from MEI.- Build reasoning and problem-solving skills with practice questions and well-structured exercises that improve statistical techniques.- Develop a fuller understanding of statistics concepts with real world examples that help build connections between topics and develop modelling skills.- Address misconceptions and develop problem-solving with annotated worked examples.- Supports you at every stage of your learning with graduated exercises that improve understanding and measure progress.