Frontiers In Interpolation And Approximation

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Frontiers in Interpolation and Approximation

N. K. Govil,H. N. Mhaskar,Ram N. Mohapatra,Zuhair Nashed,J. Szabados
Frontiers in Interpolation and Approximation Book PDF

Author : N. K. Govil,H. N. Mhaskar,Ram N. Mohapatra,Zuhair Nashed,J. Szabados
Publisher : CRC Press
Page : 476 pages
File Size : 50,5 Mb
Release : 2006-07-20
Category : Mathematics
ISBN : 9781420011388

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Frontiers in Interpolation and Approximation by N. K. Govil,H. N. Mhaskar,Ram N. Mohapatra,Zuhair Nashed,J. Szabados Pdf

Dedicated to the well-respected research mathematician Ambikeshwar Sharma, Frontiers in Interpolation and Approximation explores approximation theory, interpolation theory, and classical analysis. Written by authoritative international mathematicians, this book presents many important results in classical analysis, wavelets, and interpolation theory. Some topics covered are Markov inequalities for multivariate polynomials, analogues of Chebyshev and Bernstein inequalities for multivariate polynomials, various measures of the smoothness of functions, and the equivalence of Hausdorff continuity and pointwise Hausdorff-Lipschitz continuity of a restricted center multifunction. The book also provides basic facts about interpolation, discussing classes of entire functions such as algebraic polynomials, trigonometric polynomials, and nonperiodic transcendental entire functions. Containing both original research and comprehensive surveys, this book provides researchers and graduate students with important results of interpolation and approximation.

Frontiers in Approximation Theory

George A Anastassiou
Frontiers in Approximation Theory Book PDF

Author : George A Anastassiou
Publisher : World Scientific
Page : 228 pages
File Size : 55,9 Mb
Release : 2015-06-23
Category : Mathematics
ISBN : 9789814696111

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Frontiers in Approximation Theory by George A Anastassiou Pdf

This monograph presents the author's work of the last five years in approximation theory. The chapters are self-contained and can be read independently. Readers will find the topics covered are diverse and advanced courses can be taught out of this book. The first part of the book is dedicated to fractional monotone approximation theory introduced for the first time by the author, taking the related ordinary theory of usual differentiation at the fractional differentiation level with polynomials and splines as approximators. The second part deals with the approximation by discrete singular operators of the Favard style, for example, of the Picard and Gauss–Weierstrass types. Then, it continues in a very detailed and extensive chapter on approximation by interpolating operators induced by neural networks, a connection to computer science. This book ends with the approximation theory and functional analysis on time scales, a very modern topic, detailing all the pros and cons of this method. The results in this book are expected to find applications in many areas of pure and applied mathematics. So far, very little is written about fractional approximation theory which is at its infancy. As such, it is suitable for researchers, graduate students, and performing seminars as well as an invaluable resource for all science libraries. Contents:Fractional Monotone ApproximationRight Fractional Monotone Approximation Theory Univariate Left Fractional Polynomial High Order Monotone Approximation Theory Univariate Right Fractional Polynomial High Order Monotone Approximation TheorySpline Left Fractional Monotone Approximation Theory Using Left Fractional Differential OperatorsSpline Right Fractional Monotone Approximation Theory Using Right Fractional Differential OperatorsComplete Fractional Monotone Approximation TheoryLower Order Fractional Monotone Approximation TheoryApproximation Theory by Discrete Singular OperatorsOn Discrete Approximation by Gauss–Weierstrass and Picard Type Operators Approximation Theory by Interpolating Neural NetworksApproximation and Functional Analysis Over Time Scales Readership: Graduate students and researchers in approximation theory. Key Features:Presents new research in approximation theoryAn extensive list of references is given in every chapterIt is about fractional approximation, neural networks and singular integrals approximationsImportant to applications in applied mathematicsKeywords:Fractional Approximation;Neural Networks;Singular Integrals

Weighted Polynomial Approximation and Numerical Methods for Integral Equations

Peter Junghanns,Giuseppe Mastroianni,Incoronata Notarangelo
Weighted Polynomial Approximation and Numerical Methods for Integral Equations Book PDF

Author : Peter Junghanns,Giuseppe Mastroianni,Incoronata Notarangelo
Publisher : Springer Nature
Page : 662 pages
File Size : 40,7 Mb
Release : 2021-08-10
Category : Mathematics
ISBN : 9783030774974

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Weighted Polynomial Approximation and Numerical Methods for Integral Equations by Peter Junghanns,Giuseppe Mastroianni,Incoronata Notarangelo Pdf

The book presents a combination of two topics: one coming from the theory of approximation of functions and integrals by interpolation and quadrature, respectively, and the other from the numerical analysis of operator equations, in particular, of integral and related equations. The text focusses on interpolation and quadrature processes for functions defined on bounded and unbounded intervals and having certain singularities at the endpoints of the interval, as well as on numerical methods for Fredholm integral equations of first and second kind with smooth and weakly singular kernel functions, linear and nonlinear Cauchy singular integral equations, and hypersingular integral equations. The book includes both classic and very recent results and will appeal to graduate students and researchers who want to learn about the approximation of functions and the numerical solution of operator equations, in particular integral equations.

Frontiers of Fractal Analysis

Santo Banerjee,A. Gowrisankar
Frontiers of Fractal Analysis Book PDF

Author : Santo Banerjee,A. Gowrisankar
Publisher : CRC Press
Page : 182 pages
File Size : 42,8 Mb
Release : 2022-07-07
Category : Mathematics
ISBN : 9781000625875

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Frontiers of Fractal Analysis by Santo Banerjee,A. Gowrisankar Pdf

The history of describing natural objects using geometry is as old as the advent of science itself, in which traditional shapes are the basis of our intuitive understanding of geometry. However, nature is not restricted to such Euclidean objects which are only characterized typically by integer dimensions. Hence, the conventional geometric approach cannot meet the requirements of solving or analysing nonlinear problems which are related with natural phenomena, therefore, the fractal theory has been born, which aims to understand complexity and provide an innovative way to recognize irregularity and complex systems. Although the concepts of fractal geometry have found wide applications in many forefront areas of science, engineering and societal issues, they also have interesting implications of a more practical nature for the older classical areas of science. Since its discovery, there has been a surge of research activities in using this powerful concept in almost every branch of scientific disciplines to gain deep insights into many unresolved problems. This book includes eight chapters which focus on gathering cutting-edge research and proposing application of fractals features in both traditional scientific disciplines and in applied fields.

New Frontiers in Applied Artificial Intelligence

Leszek Borzemski,Adam Grzech,Moonis Ali
New Frontiers in Applied Artificial Intelligence Book PDF

Author : Leszek Borzemski,Adam Grzech,Moonis Ali
Publisher : Springer
Page : 879 pages
File Size : 42,6 Mb
Release : 2008-06-17
Category : Computers
ISBN : 9783540690528

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New Frontiers in Applied Artificial Intelligence by Leszek Borzemski,Adam Grzech,Moonis Ali Pdf

The 21st International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems (IEA-AIE 2008) held in Wroclaw, Poland was an international scientific forum for researchers in the field of applied artificial intelligence. The presentations of the invited speakers and the authors focused on developing and employing methods and systems to solve real-life problems in all applied intelligence areas. The IEA-AIE conference series, chaired by Moonis Ali, has a very long tradition, and it is the first time it was hosted in Poland. We received 302 papers from 52 countries. Each paper was sent to at least three Program Committee members for review. Although the general quality of the submissions was very high, only 90 best papers were selected for oral presentation and publication in the LNAI proceedings. The papers in the proceedings cover the following topics: computer vision, fuzzy system applications, robot, manufacturing, data mining and knowledge discovery, neural network, machine learning, natural language processing, Internet application, e-learning, heuristic search, application systems, agent-based system, evolutionary and genetic algorithms, knowledge management, and other applications. These papers highlight new trends and frontiers of applied artificial intelligence and show how new research could lead to new and innovative applications. We hope you will find these works useful and inspiring for your own research. We would like to express our sincere thanks to the Program Committee members and all the reviewers for their hard work, which helped us to select the highest quality papers for the conference.

Approximate Commutative Algebra

Lorenzo Robbiano,John Abbott
Approximate Commutative Algebra Book PDF

Author : Lorenzo Robbiano,John Abbott
Publisher : Springer Science & Business Media
Page : 237 pages
File Size : 40,8 Mb
Release : 2009-09-18
Category : Mathematics
ISBN : 9783211993149

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Approximate Commutative Algebra by Lorenzo Robbiano,John Abbott Pdf

Approximate Commutative Algebra is an emerging field of research which endeavours to bridge the gap between traditional exact Computational Commutative Algebra and approximate numerical computation. The last 50 years have seen enormous progress in the realm of exact Computational Commutative Algebra, and given the importance of polynomials in scientific modelling, it is very natural to want to extend these ideas to handle approximate, empirical data deriving from physical measurements of phenomena in the real world. In this volume nine contributions from established researchers describe various approaches to tackling a variety of problems arising in Approximate Commutative Algebra.

Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan

Josef Dick,Frances Y. Kuo,Henryk Woźniakowski
Contemporary Computational Mathematics A Celebration of the 80th Birthday of Ian Sloan Book PDF

Author : Josef Dick,Frances Y. Kuo,Henryk Woźniakowski
Publisher : Springer
Page : 1309 pages
File Size : 49,6 Mb
Release : 2018-05-23
Category : Mathematics
ISBN : 9783319724560

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Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan by Josef Dick,Frances Y. Kuo,Henryk Woźniakowski Pdf

This book is a tribute to Professor Ian Hugh Sloan on the occasion of his 80th birthday. It consists of nearly 60 articles written by international leaders in a diverse range of areas in contemporary computational mathematics. These papers highlight the impact and many achievements of Professor Sloan in his distinguished academic career. The book also presents state of the art knowledge in many computational fields such as quasi-Monte Carlo and Monte Carlo methods for multivariate integration, multi-level methods, finite element methods, uncertainty quantification, spherical designs and integration on the sphere, approximation and interpolation of multivariate functions, oscillatory integrals, and in general in information-based complexity and tractability, as well as in a range of other topics. The book also tells the life story of the renowned mathematician, family man, colleague and friend, who has been an inspiration to many of us. The reader may especially enjoy the story from the perspective of his family, his wife, his daughter and son, as well as grandchildren, who share their views of Ian. The clear message of the book is that Ian H. Sloan has been a role model in science and life.

Interpolation and Approximation by Rational Functions in the Complex Domain

J. L. Walsh
Interpolation and Approximation by Rational Functions in the Complex Domain Book PDF

Author : J. L. Walsh
Publisher : American Mathematical Soc.
Page : 418 pages
File Size : 40,8 Mb
Release : 1935-12-31
Category : Mathematics
ISBN : 9780821810200

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Interpolation and Approximation by Rational Functions in the Complex Domain by J. L. Walsh Pdf

The present work is restricted to the representation of functions in the complex domain, particularly analytic functions, by sequences of polynomials or of more general rational functions whose poles are preassigned, the sequences being defined either by interpolation or by extremal properties (i.e. best approximation). Taylor's series plays a central role in this entire study, for it has properties of both interpolation and best approximation, and serves as a guide throughout the whole treatise. Indeed, almost every result given on the representation of functions is concerned with a generalization either of Taylor's series or of some property of Taylor's series--the title ``Generalizations of Taylor's Series'' would be appropriate.

Frontiers in Industrial and Applied Mathematics

Rajesh Kumar Sharma,Lorenzo Pareschi,Abdon Atangana,Bikash Sahoo,Vijay Kumar Kukreja
Frontiers in Industrial and Applied Mathematics Book PDF

Author : Rajesh Kumar Sharma,Lorenzo Pareschi,Abdon Atangana,Bikash Sahoo,Vijay Kumar Kukreja
Publisher : Springer Nature
Page : 659 pages
File Size : 44,7 Mb
Release : 2023-02-02
Category : Mathematics
ISBN : 9789811972720

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Frontiers in Industrial and Applied Mathematics by Rajesh Kumar Sharma,Lorenzo Pareschi,Abdon Atangana,Bikash Sahoo,Vijay Kumar Kukreja Pdf

This book publishes select papers presented at the 4th International Conference on Frontiers in Industrial and Applied Mathematics (FIAM-2021), held at the Sant Longowal Institute of Engineering and Technology, Longowal, Punjab, India, from 21–22 December 2021. Most of the papers deal with mathematical theory embedded with its applications to engineering and sciences. This book illustrates numerical simulation of scientific problems and the state-of-the-art research in industrial and applied mathematics, including various computational and modeling techniques with case studies and concrete examples. Graduate students and researchers, who are interested in real applications of mathematics in the areas of computational and theoretical fluid dynamics, solid mechanics, optimization and operations research, numerical analysis, bio-mathematics, fuzzy, control and systems theory, dynamical systems and nonlinear analysis, algebra and approximation theory, will find the book useful.

Smart Sensors at the IoT Frontier

Hiroto Yasuura,Chong-Min Kyung,Yongpan Liu,Youn-Long Lin
Smart Sensors at the IoT Frontier Book PDF

Author : Hiroto Yasuura,Chong-Min Kyung,Yongpan Liu,Youn-Long Lin
Publisher : Springer
Page : 378 pages
File Size : 54,7 Mb
Release : 2017-05-29
Category : Technology & Engineering
ISBN : 9783319553450

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Smart Sensors at the IoT Frontier by Hiroto Yasuura,Chong-Min Kyung,Yongpan Liu,Youn-Long Lin Pdf

This book describes technology used for effective sensing of our physical world and intelligent processing techniques for sensed information, which are essential to the success of Internet of Things (IoT). The authors provide a multidisciplinary view of sensor technology from materials, process, circuits, to big data domains and they showcase smart sensor systems in real applications including smart home, transportation, medical, environmental, agricultural, etc. Unlike earlier books on sensors, this book provides a “global” view on smart sensors covering abstraction levels from device, circuit, systems, and algorithms.

Metaharmonic Lattice Point Theory

Willi Freeden
Metaharmonic Lattice Point Theory Book PDF

Author : Willi Freeden
Publisher : CRC Press
Page : 467 pages
File Size : 41,6 Mb
Release : 2011-05-09
Category : Mathematics
ISBN : 9781439861851

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Metaharmonic Lattice Point Theory by Willi Freeden Pdf

Metaharmonic Lattice Point Theory covers interrelated methods and tools of spherically oriented geomathematics and periodically reflected analytic number theory. The book establishes multi-dimensional Euler and Poisson summation formulas corresponding to elliptic operators for the adaptive determination and calculation of formulas and identities of

Direct Sum Decompositions of Torsion-Free Finite Rank Groups

Theodore G. Faticoni
Direct Sum Decompositions of Torsion Free Finite Rank Groups Book PDF

Author : Theodore G. Faticoni
Publisher : CRC Press
Page : 344 pages
File Size : 51,9 Mb
Release : 2007-03-28
Category : Mathematics
ISBN : 1584887273

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Direct Sum Decompositions of Torsion-Free Finite Rank Groups by Theodore G. Faticoni Pdf

With plenty of new material not found in other books, Direct Sum Decompositions of Torsion-Free Finite Rank Groups explores advanced topics in direct sum decompositions of abelian groups and their consequences. The book illustrates a new way of studying these groups while still honoring the rich history of unique direct sum decompositions of groups

Matrix Theory

Robert Piziak,P.L. Odell
Matrix Theory Book PDF

Author : Robert Piziak,P.L. Odell
Publisher : CRC Press
Page : 570 pages
File Size : 43,7 Mb
Release : 2007-02-22
Category : Mathematics
ISBN : 9781584886259

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Matrix Theory by Robert Piziak,P.L. Odell Pdf

In 1990, the National Science Foundation recommended that every college mathematics curriculum should include a second course in linear algebra. In answer to this recommendation, Matrix Theory: From Generalized Inverses to Jordan Form provides the material for a second semester of linear algebra that probes introductory linear algebra concepts while also exploring topics not typically covered in a sophomore-level class. Tailoring the material to advanced undergraduate and beginning graduate students, the authors offer instructors flexibility in choosing topics from the book. The text first focuses on the central problem of linear algebra: solving systems of linear equations. It then discusses LU factorization, derives Sylvester's rank formula, introduces full-rank factorization, and describes generalized inverses. After discussions on norms, QR factorization, and orthogonality, the authors prove the important spectral theorem. They also highlight the primary decomposition theorem, Schur's triangularization theorem, singular value decomposition, and the Jordan canonical form theorem. The book concludes with a chapter on multilinear algebra. With this classroom-tested text students can delve into elementary linear algebra ideas at a deeper level and prepare for further study in matrix theory and abstract algebra.

Algorithmic Lie Theory for Solving Ordinary Differential Equations

Fritz Schwarz
Algorithmic Lie Theory for Solving Ordinary Differential Equations Book PDF

Author : Fritz Schwarz
Publisher : CRC Press
Page : 448 pages
File Size : 43,8 Mb
Release : 2007-10-02
Category : Mathematics
ISBN : 1584888903

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Algorithmic Lie Theory for Solving Ordinary Differential Equations by Fritz Schwarz Pdf

Despite the fact that Sophus Lie's theory was virtually the only systematic method for solving nonlinear ordinary differential equations (ODEs), it was rarely used for practical problems because of the massive amount of calculations involved. But with the advent of computer algebra programs, it became possible to apply Lie theory to concrete proble

Noncommutative Geometry and Cayley-smooth Orders

Lieven Le Bruyn
Noncommutative Geometry and Cayley smooth Orders Book PDF

Author : Lieven Le Bruyn
Publisher : CRC Press
Page : 592 pages
File Size : 54,7 Mb
Release : 2007-08-24
Category : Mathematics
ISBN : 9781420064230

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Noncommutative Geometry and Cayley-smooth Orders by Lieven Le Bruyn Pdf

Noncommutative Geometry and Cayley-smooth Orders explains the theory of Cayley-smooth orders in central simple algebras over function fields of varieties. In particular, the book describes the etale local structure of such orders as well as their central singularities and finite dimensional representations. After an introduction to partial d