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Intelligent Mathematics Ii Applied Mathematics And Approximation Theory
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Book Synopsis Intelligent Mathematics II: Applied Mathematics and Approximation Theory by : George A. Anastassiou
Download or read book Intelligent Mathematics II: Applied Mathematics and Approximation Theory written by George A. Anastassiou and published by Springer. This book was released on 2016-03-21 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: This special volume is a collection of outstanding more applied articles presented in AMAT 2015 held in Ankara, May 28-31, 2015, at TOBB Economics and Technology University. The collection is suitable for Applied and Computational Mathematics and Engineering practitioners, also for related graduate students and researchers. Furthermore it will be a useful resource for all science and engineering libraries. This book includes 29 self-contained and well-edited chapters that can be among others useful for seminars in applied and computational mathematics, as well as in engineering.
Book Synopsis Intelligent Comparisons II: Operator Inequalities and Approximations by : George A. Anastassiou
Download or read book Intelligent Comparisons II: Operator Inequalities and Approximations written by George A. Anastassiou and published by Springer. This book was released on 2017-01-13 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This compact book focuses on self-adjoint operators’ well-known named inequalities and Korovkin approximation theory, both in a Hilbert space environment. It is the first book to study these aspects, and all chapters are self-contained and can be read independently. Further, each chapter includes an extensive list of references for further reading. The book’s results are expected to find applications in many areas of pure and applied mathematics. Given its concise format, it is especially suitable for use in related graduate classes and research projects. As such, the book offers a valuable resource for researchers and graduate students alike, as well as a key addition to all science and engineering libraries.
Author :George A. Anastassiou Publisher :Springer Science & Business Media ISBN 13 :3642170986 Total Pages :793 pages Book Rating :4.6/5 (421 download)
Book Synopsis Intelligent Mathematics: Computational Analysis by : George A. Anastassiou
Download or read book Intelligent Mathematics: Computational Analysis written by George A. Anastassiou and published by Springer Science & Business Media. This book was released on 2011-03-19 with total page 793 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knowledge can be modeled and computed using computational mathematical methods, then lead to real world conclusions. The strongly related to that Computational Analysis is a very large area with lots of applications. This monograph includes a great variety of topics of Computational Analysis. We present: probabilistic wavelet approximations, constrained abstract approximation theory, shape preserving weighted approximation, non positive approximations to definite integrals, discrete best approximation, approximation theory of general Picard singular operators including global smoothness preservation property, fractional singular operators. We also deal with non-isotropic general Picard singular multivariate operators and q-Gauss-Weierstrass singular q-integral operators. We talk about quantitative approximations by shift-invariant univariate and multivariate integral operators, nonlinear neural networks approximation, convergence with rates of positive linear operators, quantitative approximation by bounded linear operators, univariate and multivariate quantitative approximation by stochastic positive linear operators on univariate and multivariate stochastic processes. We further present right fractional calculus and give quantitative fractional Korovkin theory of positive linear operators. We also give analytical inequalities, fractional Opial inequalities, fractional identities and inequalities regarding fractional integrals. We further deal with semi group operator approximation, simultaneous Feller probabilistic approximation. We also present Fuzzy singular operator approximations. We give transfers from real to fuzzy approximation and talk about fuzzy wavelet and fuzzy neural networks approximations, fuzzy fractional calculus and fuzzy Ostrowski inequality. We talk about discrete fractional calculus, nabla discrete fractional calculus and inequalities. We study the q-inequalities, and q-fractional inequalities. We further study time scales: delta and nabla approaches, duality principle and inequalities. We introduce delta and nabla time scales fractional calculus and inequalities. We finally study convergence with rates of approximate solutions to exact solution of multivariate Dirichlet problem and multivariate heat equation, and discuss the uniqueness of solution of general evolution partial differential equation \ in multivariate time. The exposed results are expected to find applications to: applied and computational mathematics, stochastics, engineering, artificial intelligence, vision, complexity and machine learning. This monograph is suitable for graduate students and researchers.
Book Synopsis Foundations of Applied Mathematics, Volume 2 by : Jeffrey Humpherys
Download or read book Foundations of Applied Mathematics, Volume 2 written by Jeffrey Humpherys and published by SIAM. This book was released on 2020-03-10 with total page 806 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this second book of what will be a four-volume series, the authors present, in a mathematically rigorous way, the essential foundations of both the theory and practice of algorithms, approximation, and optimization—essential topics in modern applied and computational mathematics. This material is the introductory framework upon which algorithm analysis, optimization, probability, statistics, machine learning, and control theory are built. This text gives a unified treatment of several topics that do not usually appear together: the theory and analysis of algorithms for mathematicians and data science students; probability and its applications; the theory and applications of approximation, including Fourier series, wavelets, and polynomial approximation; and the theory and practice of optimization, including dynamic optimization. When used in concert with the free supplemental lab materials, Foundations of Applied Mathematics, Volume 2: Algorithms, Approximation, Optimization teaches not only the theory but also the computational practice of modern mathematical methods. Exercises and examples build upon each other in a way that continually reinforces previous ideas, allowing students to retain learned concepts while achieving a greater depth. The mathematically rigorous lab content guides students to technical proficiency and answers the age-old question “When am I going to use this?” This textbook is geared toward advanced undergraduate and beginning graduate students in mathematics, data science, and machine learning.
Author :George A. Anastassiou Publisher :Springer Science & Business Media ISBN 13 :3642214312 Total Pages :113 pages Book Rating :4.6/5 (422 download)
Book Synopsis Intelligent Systems: Approximation by Artificial Neural Networks by : George A. Anastassiou
Download or read book Intelligent Systems: Approximation by Artificial Neural Networks written by George A. Anastassiou and published by Springer Science & Business Media. This book was released on 2011-06-02 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief monograph is the first one to deal exclusively with the quantitative approximation by artificial neural networks to the identity-unit operator. Here we study with rates the approximation properties of the "right" sigmoidal and hyperbolic tangent artificial neural network positive linear operators. In particular we study the degree of approximation of these operators to the unit operator in the univariate and multivariate cases over bounded or unbounded domains. This is given via inequalities and with the use of modulus of continuity of the involved function or its higher order derivative. We examine the real and complex cases. For the convenience of the reader, the chapters of this book are written in a self-contained style. This treatise relies on author's last two years of related research work. Advanced courses and seminars can be taught out of this brief book. All necessary background and motivations are given per chapter. A related list of references is given also per chapter. The exposed results are expected to find applications in many areas of computer science and applied mathematics, such as neural networks, intelligent systems, complexity theory, learning theory, vision and approximation theory, etc. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, also for all science libraries.
Author :George A. Anastassiou Publisher :Springer Science & Business Media ISBN 13 :3642198260 Total Pages :239 pages Book Rating :4.6/5 (421 download)
Book Synopsis Towards Intelligent Modeling: Statistical Approximation Theory by : George A. Anastassiou
Download or read book Towards Intelligent Modeling: Statistical Approximation Theory written by George A. Anastassiou and published by Springer Science & Business Media. This book was released on 2011-04-06 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main idea of statistical convergence is to demand convergence only for a majority of elements of a sequence. This method of convergence has been investigated in many fundamental areas of mathematics such as: measure theory, approximation theory, fuzzy logic theory, summability theory, and so on. In this monograph we consider this concept in approximating a function by linear operators, especially when the classical limit fails. The results of this book not only cover the classical and statistical approximation theory, but also are applied in the fuzzy logic via the fuzzy-valued operators. The authors in particular treat the important Korovkin approximation theory of positive linear operators in statistical and fuzzy sense. They also present various statistical approximation theorems for some specific real and complex-valued linear operators that are not positive. This is the first monograph in Statistical Approximation Theory and Fuzziness. The chapters are self-contained and several advanced courses can be taught. The research findings will be useful in various applications including applied and computational mathematics, stochastics, engineering, artificial intelligence, vision and machine learning. This monograph is directed to graduate students, researchers, practitioners and professors of all disciplines.
Book Synopsis Foundations of Computational Intelligence Volume 5 by : Ajith Abraham
Download or read book Foundations of Computational Intelligence Volume 5 written by Ajith Abraham and published by Springer. This book was released on 2009-07-11 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundations of Computational Intelligence Volume 5: Function Approximation and Classification Approximation theory is that area of analysis which is concerned with the ability to approximate functions by simpler and more easily calculated functions. It is an area which, like many other fields of analysis, has its primary roots in the mat- matics. The need for function approximation and classification arises in many branches of applied mathematics, computer science and data mining in particular. This edited volume comprises of 14 chapters, including several overview Ch- ters, which provides an up-to-date and state-of-the art research covering the theory and algorithms of function approximation and classification. Besides research ar- cles and expository papers on theory and algorithms of function approximation and classification, papers on numerical experiments and real world applications were also encouraged. The Volume is divided into 2 parts: Part-I: Function Approximation and Classification – Theoretical Foundations Part-II: Function Approximation and Classification – Success Stories and Real World Applications Part I on Function Approximation and Classification – Theoretical Foundations contains six chapters that describe several approaches Feature Selection, the use Decomposition of Correlation Integral, Some Issues on Extensions of Information and Dynamic Information System and a Probabilistic Approach to the Evaluation and Combination of Preferences Chapter 1 “Feature Selection for Partial Least Square Based Dimension Red- tion” by Li and Zeng investigate a systematic feature reduction framework by combing dimension reduction with feature selection. To evaluate the proposed framework authors used four typical data sets.
Book Synopsis Abstract Fractional Monotone Approximation, Theory and Applications by : George A. Anastassiou
Download or read book Abstract Fractional Monotone Approximation, Theory and Applications written by George A. Anastassiou and published by Springer Nature. This book was released on 2022-03-11 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book employs an abstract kernel fractional calculus with applications to Prabhakar and non-singular kernel fractional calculi. The results are univariate and bivariate. In the univariate case, abstract fractional monotone approximation by polynomials and splines is presented. In the bivariate case, the abstract fractional monotone constrained approximation by bivariate pseudo-polynomials and polynomials is given. This book’s results are expected to find applications in many areas of pure and applied mathematics, especially in fractional approximation and fractional differential equations. Other interesting applications are applied in sciences like geophysics, physics, chemistry, economics, and engineering. This book is appropriate for researchers, graduate students, practitioners, and seminars of the above disciplines.
Book Synopsis Intelligent Systems II: Complete Approximation by Neural Network Operators by : George A. Anastassiou
Download or read book Intelligent Systems II: Complete Approximation by Neural Network Operators written by George A. Anastassiou and published by Springer. This book was released on 2015-06-23 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is the continuation and completion of the monograph, “Intelligent Systems: Approximation by Artificial Neural Networks” written by the same author and published 2011 by Springer. The book you hold in hand presents the complete recent and original work of the author in approximation by neural networks. Chapters are written in a self-contained style and can be read independently. Advanced courses and seminars can be taught out of this brief book. All necessary background and motivations are given per chapter. A related list of references is given also per chapter. The book’s results are expected to find applications in many areas of applied mathematics, computer science and engineering. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, also for all science and engineering libraries.
Book Synopsis Bayesian Reasoning and Gaussian Processes for Machine Learning Applications by : Hemachandran K
Download or read book Bayesian Reasoning and Gaussian Processes for Machine Learning Applications written by Hemachandran K and published by CRC Press. This book was released on 2022-04-14 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces Bayesian reasoning and Gaussian processes into machine learning applications. Bayesian methods are applied in many areas, such as game development, decision making, and drug discovery. It is very effective for machine learning algorithms in handling missing data and extracting information from small datasets. Bayesian Reasoning and Gaussian Processes for Machine Learning Applications uses a statistical background to understand continuous distributions and how learning can be viewed from a probabilistic framework. The chapters progress into such machine learning topics as belief network and Bayesian reinforcement learning, which is followed by Gaussian process introduction, classification, regression, covariance, and performance analysis of Gaussian processes with other models. FEATURES Contains recent advancements in machine learning Highlights applications of machine learning algorithms Offers both quantitative and qualitative research Includes numerous case studies This book is aimed at graduates, researchers, and professionals in the field of data science and machine learning.
Book Synopsis Mathematical Methods in Engineering by : Kenan Taş
Download or read book Mathematical Methods in Engineering written by Kenan Taş and published by Springer. This book was released on 2018-08-02 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent developments in nonlinear dynamics with an emphasis on complex systems. The volume illustrates new methods to characterize the solutions of nonlinear dynamics associated with complex systems. This book contains the following topics: new solutions of the functional equations, optimization algorithm for traveling salesman problem, fractals, control, fractional calculus models, fractional discretization, local fractional partial differential equations and their applications, and solutions of fractional kinetic equations.
Book Synopsis Issues in the Use of Neural Networks in Information Retrieval by : Iuliana F. Iatan
Download or read book Issues in the Use of Neural Networks in Information Retrieval written by Iuliana F. Iatan and published by Springer. This book was released on 2016-09-28 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights the ability of neural networks (NNs) to be excellent pattern matchers and their importance in information retrieval (IR), which is based on index term matching. The book defines a new NN-based method for learning image similarity and describes how to use fuzzy Gaussian neural networks to predict personality.It introduces the fuzzy Clifford Gaussian network, and two concurrent neural models: (1) concurrent fuzzy nonlinear perceptron modules, and (2) concurrent fuzzy Gaussian neural network modules.Furthermore, it explains the design of a new model of fuzzy nonlinear perceptron based on alpha level sets and describes a recurrent fuzzy neural network model with a learning algorithm based on the improved particle swarm optimization method.
Book Synopsis Intelligent Analysis: Fractional Inequalities and Approximations Expanded by : George A. Anastassiou
Download or read book Intelligent Analysis: Fractional Inequalities and Approximations Expanded written by George A. Anastassiou and published by Springer Nature. This book was released on 2020-01-15 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on computational and fractional analysis, two areas that are very important in their own right, and which are used in a broad variety of real-world applications. We start with the important Iyengar type inequalities and we continue with Choquet integral analytical inequalities, which are involved in major applications in economics. In turn, we address the local fractional derivatives of Riemann–Liouville type and related results including inequalities. We examine the case of low order Riemann–Liouville fractional derivatives and inequalities without initial conditions, together with related approximations. In the next section, we discuss quantitative complex approximation theory by operators and various important complex fractional inequalities. We also cover the conformable fractional approximation of Csiszar’s well-known f-divergence, and present conformable fractional self-adjoint operator inequalities. We continue by investigating new local fractional M-derivatives that share all the basic properties of ordinary derivatives. In closing, we discuss the new complex multivariate Taylor formula with integral remainder. Sharing results that can be applied in various areas of pure and applied mathematics, the book offers a valuable resource for researchers and graduate students, and can be used to support seminars in related fields.
Book Synopsis Recent Advances in Intelligent Information Systems and Applied Mathematics by : Oscar Castillo
Download or read book Recent Advances in Intelligent Information Systems and Applied Mathematics written by Oscar Castillo and published by Springer Nature. This book was released on 2020-01-31 with total page 903 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the latest advances in intelligent techniques such as fuzzy logic, neural networks, and optimization algorithms, and their relevance in building intelligent information systems in combination with applied mathematics. The authors also outline the applications of these systems in areas like intelligent control and robotics, pattern recognition, medical diagnosis, time series prediction, and optimization of complex problems. By sharing fresh ideas and identifying new targets/problems it offers young researchers and students new directions for their future research. The book is intended for readers from mathematics and computer science, in particular professors and students working on theory and applications of intelligent systems for real-world applications.
Book Synopsis 4th International Conference on Artificial Intelligence and Applied Mathematics in Engineering by : D. Jude Hemanth
Download or read book 4th International Conference on Artificial Intelligence and Applied Mathematics in Engineering written by D. Jude Hemanth and published by Springer Nature. This book was released on 2023-07-02 with total page 779 pages. Available in PDF, EPUB and Kindle. Book excerpt: As general, this book is a collection of the most recent, quality research papers regarding applications of Artificial Intelligence and Applied Mathematics for engineering problems. The papers included in the book were accepted and presented in the 4th International Conference on Artificial Intelligence and Applied Mathematics in Engineering (ICAIAME 2022), which was held in Baku, Azerbaijan (Azerbaijan Technical University) between May 20 and 22, 2022. Objective of the book content is to inform the international audience about the cutting-edge, effective developments and improvements in different engineering fields. As a collection of the ICAIAME 2022 event, the book gives consideration for the results by especially intelligent system formations and the associated applications. The target audience of the book is international researchers, degree students, practitioners from industry, and experts from different engineering disciplines.
Book Synopsis Advances in Mathematical Modelling, Applied Analysis and Computation by : Jagdev Singh
Download or read book Advances in Mathematical Modelling, Applied Analysis and Computation written by Jagdev Singh and published by Springer Nature. This book was released on with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Intelligent Numerical Methods: Applications to Fractional Calculus by : George A. Anastassiou
Download or read book Intelligent Numerical Methods: Applications to Fractional Calculus written by George A. Anastassiou and published by Springer. This book was released on 2015-12-07 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph the authors present Newton-type, Newton-like and other numerical methods, which involve fractional derivatives and fractional integral operators, for the first time studied in the literature. All for the purpose to solve numerically equations whose associated functions can be also non-differentiable in the ordinary sense. That is among others extending the classical Newton method theory which requires usual differentiability of function. Chapters are self-contained and can be read independently and several advanced courses can be taught out of this book. An extensive list of references is given per chapter. The book’s results are expected to find applications in many areas of applied mathematics, stochastics, computer science and engineering. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, also to be in all science and engineering libraries.
