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Computational Functional Analysis

Computational Functional Analysis Book
Author : Ramon E Moore,Michael J Cloud
Publisher : Elsevier
Release : 2007-06-01
ISBN : 0857099434
Language : En, Es, Fr & De

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Book Description :

This course text fills a gap for first-year graduate-level students reading applied functional analysis or advanced engineering analysis and modern control theory. Containing 100 problem-exercises, answers, and tutorial hints, the first edition is often cited as a standard reference. Making a unique contribution to numerical analysis for operator equations, it introduces interval analysis into the mainstream of computational functional analysis, and discusses the elegant techniques for reproducing Kernel Hilbert spaces. There is discussion of a successful ‘‘hybrid’’ method for difficult real-life problems, with a balance between coverage of linear and non-linear operator equations. The authors successful teaching philosophy: ‘‘We learn by doing’’ is reflected throughout the book. Contains 100 problem-exercises, answers and tutorial hints for students reading applied functional analysis Introduces interval analysis into the mainstream of computational functional analysis

An Introduction to Functional Analysis in Computational Mathematics

An Introduction to Functional Analysis in Computational Mathematics Book
Author : V.I. Lebedev
Publisher : Birkhäuser
Release : 2011-09-26
ISBN : 9781461286660
Language : En, Es, Fr & De

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Book Description :

The book contains the methods and bases of functional analysis that are directly adjacent to the problems of numerical mathematics and its applications; they are what one needs for the understand ing from a general viewpoint of ideas and methods of computational mathematics and of optimization problems for numerical algorithms. Functional analysis in mathematics is now just the small visible part of the iceberg. Its relief and summit were formed under the influence of this author's personal experience and tastes. This edition in English contains some additions and changes as compared to the second edition in Russian; discovered errors and misprints had been corrected again here; to the author's distress, they jump incomprehensibly from one edition to another as fleas. The list of literature is far from being complete; just a number of textbooks and monographs published in Russian have been included. The author is grateful to S. Gerasimova for her help and patience in the complex process of typing the mathematical manuscript while the author corrected, rearranged, supplemented, simplified, general ized, and improved as it seemed to him the book's contents. The author thanks G. Kontarev for the difficult job of translation and V. Klyachin for the excellent figures.

Computational Functional Analysis

Computational Functional Analysis Book
Author : Ramon E. Moore
Publisher : Ellis Horwood Limited
Release : 1985-02-01
ISBN : 9780131426139
Language : En, Es, Fr & De

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Book Description :

Download Computational Functional Analysis book written by Ramon E. Moore, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Computational and Experimental Analysis of Functional Materials

Computational and Experimental Analysis of Functional Materials Book
Author : Oleksandr V. Reshetnyak,Gennady E. Zaikov
Publisher : CRC Press
Release : 2017-03-27
ISBN : 177188343X
Language : En, Es, Fr & De

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Book Description :

This book looks at the synthesis of polyaniline by different methods, under different conditions, for various applications, and presents studies of its properties by a wide range of the modern physic-chemical methods. The book provides a comprehensive analysis of experimental results from the point of view of the correlations in the triad synthesis conditions–structurephysico–chemical properties. It combines the results of experimental investigations and original methodology of the description of physical–chemical and electrochemical phenomena at interface surfaces, showing an influence of such phenomena on the applied aspects of the polyaniline and nanocomposites on its basis applications.

Computational and Analytical Mathematics

Computational and Analytical Mathematics Book
Author : David H. Bailey,Heinz H. Bauschke,Peter Borwein,Frank Garvan,Michel Théra,Jon D. Vanderwerff,Henry Wolkowicz
Publisher : Springer Science & Business Media
Release : 2013-09-15
ISBN : 1461476216
Language : En, Es, Fr & De

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Book Description :

The research of Jonathan Borwein has had a profound impact on optimization, functional analysis, operations research, mathematical programming, number theory, and experimental mathematics. Having authored more than a dozen books and more than 300 publications, Jonathan Borwein is one of the most productive Canadian mathematicians ever. His research spans pure, applied, and computational mathematics as well as high performance computing, and continues to have an enormous impact: MathSciNet lists more than 2500 citations by more than 1250 authors, and Borwein is one of the 250 most cited mathematicians of the period 1980-1999. He has served the Canadian Mathematics Community through his presidency (2000–02) as well as his 15 years of editing the CMS book series. Jonathan Borwein’s vision and initiative have been crucial in initiating and developing several institutions that provide support for researchers with a wide range of scientific interests. A few notable examples include the Centre for Experimental and Constructive Mathematics and the IRMACS Centre at Simon Fraser University, the Dalhousie Distributed Research Institute at Dalhousie University, the Western Canada Research Grid, and the Centre for Computer Assisted Research Mathematics and its Applications, University of Newcastle. The workshops that were held over the years in Dr. Borwein’s honor attracted high-caliber scientists from a wide range of mathematical fields. This present volume is an outgrowth of the workshop on ‘Computational and Analytical Mathematics’ held in May 2011 in celebration of Dr. Borwein’s 60th Birthday. The collection contains various state-of-the-art research manuscripts and surveys presenting contributions that have risen from the conference, and is an excellent opportunity to survey state-of-the-art research and discuss promising research directions and approaches.

Computational Text Analysis

Computational Text Analysis Book
Author : Soumya Raychaudhuri
Publisher : OUP Oxford
Release : 2006-01-26
ISBN : 0191513776
Language : En, Es, Fr & De

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Book Description :

This book brings together the two disparate worlds of computational text analysis and biology and presents some of the latest methods and applications to proteomics, sequence analysis and gene expression data. Modern genomics generates large and comprehensive data sets but their interpretation requires an understanding of a vast number of genes, their complex functions, and interactions. Keeping up with the literature on a single gene is a challenge itself-for thousands of genes it is simply. impossible. Here, Soumya Raychaudhuri presents the techniques and algorithms needed to access and utilize the vast scientific text, i.e. methods that automatically read the literature on all the genes. Including background chapters on the necessary biology, statistics and genomics, in addition to practical examples of interpreting many different types of modern experiments, this book is ideal for students and researchers in computational biology, bioinformatics, genomics, statistics and computer science

Introductory Functional Analysis with Applications

Introductory Functional Analysis with Applications Book
Author : Erwin Kreyszig
Publisher : John Wiley & Sons
Release : 1991-01-16
ISBN : 0471504599
Language : En, Es, Fr & De

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Book Description :

KREYSZIG The Wiley Classics Library consists of selected books originally published by John Wiley & Sons that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: Emil Artin Geometnc Algebra R. W. Carter Simple Groups Of Lie Type Richard Courant Differential and Integrai Calculus. Volume I Richard Courant Differential and Integral Calculus. Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics. Volume II Harold M. S. Coxeter Introduction to Modern Geometry. Second Edition Charles W. Curtis, Irving Reiner Representation Theory of Finite Groups and Associative Algebras Nelson Dunford, Jacob T. Schwartz unear Operators. Part One. General Theory Nelson Dunford. Jacob T. Schwartz Linear Operators, Part Two. Spectral Theory—Self Adjant Operators in Hilbert Space Nelson Dunford, Jacob T. Schwartz Linear Operators. Part Three. Spectral Operators Peter HenriCi Applied and Computational Complex Analysis. Volume I—Power Senes-lntegrauon-Contormal Mapping-Locatvon of Zeros Peter Hilton, Yet-Chiang Wu A Course in Modern Algebra Harry Hochstadt Integral Equations Erwin Kreyszig Introductory Functional Analysis with Applications P. M. Prenter Splines and Variational Methods C. L. Siegel TOPICS in Complex Function Theory. Volume I —Elliptic Functions and Uniformizatton Theory C. L. Siegel Topics in Complex Function Theory. Volume II —Automorphic and Abelian Integrals C. L. Siegel TOPICS In Complex Function Theory. Volume III —Abelian Functions & Modular Functions of Several Variables J. J. Stoker Differential Geometry

Basic Analysis V

Basic Analysis V Book
Author : James K. Peterson
Publisher : CRC Press
Release : 2021-08-20
ISBN : 1351679155
Language : En, Es, Fr & De

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Book Description :

Basic Analysis V: Functional Analysis and Topology introduces graduate students in science to concepts from topology and functional analysis, both linear and nonlinear. It is the fifth book in a series designed to train interested readers how to think properly using mathematical abstractions, and how to use the tools of mathematical analysis in applications. It is important to realize that the most difficult part of applying mathematical reasoning to a new problem domain is choosing the underlying mathematical framework to use on the problem. Once that choice is made, we have many tools we can use to solve the problem. However, a different choice would open up avenues of analysis from a different, perhaps more productive, perspective. In this volume, the nature of these critical choices is discussed using applications involving the immune system and cognition. Features Develops a proof of the Jordan Canonical form to show some basic ideas in algebraic topology Provides a thorough treatment of topological spaces, finishing with the Krein–Milman theorem Discusses topological degree theory (Brouwer, Leray–Schauder, and Coincidence) Carefully develops manifolds and functions on manifolds ending with Riemannian metrics Suitable for advanced students in mathematics and associated disciplines Can be used as a traditional textbook as well as for self-study Author James K. Peterson is an Emeritus Professor at the School of Mathematical and Statistical Sciences, Clemson University. He tries hard to build interesting models of complex phenomena using a blend of mathematics, computation, and science. To this end, he has written four books on how to teach such things to biologists and cognitive scientists. These books grew out of his Calculus for Biologists courses offered to the biology majors from 2007 to 2015. He has taught the analysis courses since he started teaching both at Clemson and at his previous post at Michigan Technological University. In between, he spent time as a senior engineer in various aerospace firms and even did a short stint in a software development company. The problems he was exposed to were very hard, and not amenable to solution using just one approach. Using tools from many branches of mathematics, from many types of computational languages, and from first-principles analysis of natural phenomena was absolutely essential to make progress. In both mathematical and applied areas, students often need to use advanced mathematics tools they have not learned properly. So, he has recently written a series of five books on mathematical analysis to help researchers with the problem of learning new things after they have earned their degrees and are practicing scientists. Along the way, he has also written papers in immunology, cognitive science, and neural network technology, in addition to having grants from the NSF, NASA, and the US Army. He also likes to paint, build furniture, and write stories.

Computational Mathematics and Variational Analysis

Computational Mathematics and Variational Analysis Book
Author : Nicholas J. Daras,Themistocles M. Rassias
Publisher : Springer
Release : 2021-06-06
ISBN : 9783030446277
Language : En, Es, Fr & De

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Book Description :

This volume presents a broad discussion of computational methods and theories on various classical and modern research problems from pure and applied mathematics. Readers conducting research in mathematics, engineering, physics, and economics will benefit from the diversity of topics covered. Contributions from an international community treat the following subjects: calculus of variations, optimization theory, operations research, game theory, differential equations, functional analysis, operator theory, approximation theory, numerical analysis, asymptotic analysis, and engineering. Specific topics include algorithms for difference of monotone operators, variational inequalities in semi-inner product spaces, function variation principles and normed minimizers, equilibria of parametrized N-player nonlinear games, multi-symplectic numerical schemes for differential equations, time-delay multi-agent systems, computational methods in non-linear design of experiments, unsupervised stochastic learning, asymptotic statistical results, global-local transformation, scattering relations of elastic waves, generalized Ostrowski and trapezoid type rules, numerical approximation, Szász Durrmeyer operators and approximation, integral inequalities, behaviour of the solutions of functional equations, functional inequalities in complex Banach spaces, functional contractions in metric spaces.

Applied Functional Analysis

Applied Functional Analysis Book
Author : J. Tinsley Oden,Leszek Demkowicz
Publisher : CRC Press
Release : 2017-12-01
ISBN : 149876116X
Language : En, Es, Fr & De

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Book Description :

Applied Functional Analysis, Third Edition provides a solid mathematical foundation for the subject. It motivates students to study functional analysis by providing many contemporary applications and examples drawn from mechanics and science. This well-received textbook starts with a thorough introduction to modern mathematics before continuing with detailed coverage of linear algebra, Lebesque measure and integration theory, plus topology with metric spaces. The final two chapters provides readers with an in-depth look at the theory of Banach and Hilbert spaces before concluding with a brief introduction to Spectral Theory. The Third Edition is more accessible and promotes interest and motivation among students to prepare them for studying the mathematical aspects of numerical analysis and the mathematical theory of finite elements.

Functional Analysis and Numerical Mathematics

Functional Analysis and Numerical Mathematics Book
Author : Lothar Collatz
Publisher : Academic Press
Release : 2014-05-12
ISBN : 1483264009
Language : En, Es, Fr & De

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Book Description :

Functional Analysis and Numerical Mathematics focuses on the structural changes which numerical analysis has undergone, including iterative methods, vectors, integral equations, matrices, and boundary value problems. The publication first examines the foundations of functional analysis and applications, including various types of spaces, convergence and completeness, operators in Hilbert spaces, vector and matrix norms, eigenvalue problems, and operators in pseudometric and other special spaces. The text then elaborates on iterative methods. Topics include the fixed-point theorem for a general iterative method in pseudometric spaces; special cases of the fixed-point theorem and change of operator; iterative methods for differential and integral equations; and systems of equations and difference methods. The manuscript takes a look at monotonicity, inequalities, and other topics, including monotone operators, applications of Schauder's theorem, matrices and boundary value problems of monotone kind, discrete Chebyshev approximation and exchange methods, and approximation of functions. The publication is a valuable source of data for mathematicians and researchers interested in functional analysis and numerical mathematics.

Physical Computation

Physical Computation Book
Author : Gualtiero Piccinini
Publisher : OUP Oxford
Release : 2015-07-02
ISBN : 0191633429
Language : En, Es, Fr & De

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Book Description :

Gualtiero Piccinini articulates and defends a mechanistic account of concrete, or physical, computation. A physical system is a computing system just in case it is a mechanism one of whose functions is to manipulate vehicles based solely on differences between different portions of the vehicles according to a rule defined over the vehicles. The Nature of Computation discusses previous accounts of computation and argues that the mechanistic account is better. Many kinds of computation are explicated, such as digital vs. analog, serial vs. parallel, neural network computation, program-controlled computation, and more. Piccinini argues that computation does not entail representation or information processing although information processing entails computation. Pancomputationalism, according to which every physical system is computational, is rejected. A modest version of the physical Church-Turing thesis, according to which any function that is physically computable is computable by Turing machines, is defended.

An Introduction to Functional Analysis in Computational Mathematics

An Introduction to Functional Analysis in Computational Mathematics Book
Author : Vi͡acheslav Ivanovich Lebedev
Publisher : Unknown
Release : 1997
ISBN : 9783764338886
Language : En, Es, Fr & De

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Book Description :

A text for students who are familiar with advanced and numerical mathematics, initial value problems for differential equations, elements of the theory of functions of real variables, and methods of linear algebra. Covers functional spaces and problems in the theory of approximations, linear operators and functionals, and iteration methods for solving operator equations. Translated and corrected from the second edition of Funktsional 'nyi analiz in vychislitel'naia matematika for which no date is noted. Annotation copyrighted by Book News, Inc., Portland, OR

Functional Analysis in Modern Applied Mathematics

Functional Analysis in Modern Applied Mathematics Book
Author : Anonim
Publisher : Academic Press
Release : 1977-08-24
ISBN : 9780080956411
Language : En, Es, Fr & De

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Book Description :

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

Functional Analysis in Applied Mathematics and Engineering

Functional Analysis in Applied Mathematics and Engineering Book
Author : Michael Pedersen
Publisher : Routledge
Release : 2018-10-03
ISBN : 1351446908
Language : En, Es, Fr & De

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Book Description :

Presenting excellent material for a first course on functional analysis , Functional Analysis in Applied Mathematics and Engineering concentrates on material that will be useful to control engineers from the disciplines of electrical, mechanical, and aerospace engineering. This text/reference discusses: rudimentary topology Banach's fixed point theorem with applications L^p-spaces density theorems for testfunctions infinite dimensional spaces bounded linear operators Fourier series open mapping and closed graph theorems compact and differential operators Hilbert-Schmidt operators Volterra equations Sobolev spaces control theory and variational analysis Hilbert Uniqueness Method boundary element methods Functional Analysis in Applied Mathematics and Engineering begins with an introduction to the important, abstract basic function spaces and operators with mathematical rigor, then studies problems in the Hilbert space setting. The author proves the spectral theorem for unbounded operators with compact inverses and goes on to present the abstract evolution semigroup theory for time dependent linear partial differential operators. This structure establishes a firm foundation for the more advanced topics discussed later in the text.

A Functional Analysis Framework for Modeling Estimation and Control in Science and Engineering

A Functional Analysis Framework for Modeling  Estimation and Control in Science and Engineering Book
Author : H.T. Banks
Publisher : CRC Press
Release : 2012-06-18
ISBN : 1439880840
Language : En, Es, Fr & De

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Book Description :

A Modern Framework Based on Time-Tested MaterialA Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering presents functional analysis as a tool for understanding and treating distributed parameter systems. Drawing on his extensive research and teaching from the past 20 years, the author explains how functional

Computational Methods for Deep Learning

Computational Methods for Deep Learning Book
Author : Wei Qi Yan
Publisher : Springer Nature
Release : 2020-12-04
ISBN : 3030610810
Language : En, Es, Fr & De

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Book Description :

Integrating concepts from deep learning, machine learning, and artificial neural networks, this highly unique textbook presents content progressively from easy to more complex, orienting its content about knowledge transfer from the viewpoint of machine intelligence. It adopts the methodology from graphical theory, mathematical models, and algorithmic implementation, as well as covers datasets preparation, programming, results analysis and evaluations. Beginning with a grounding about artificial neural networks with neurons and the activation functions, the work then explains the mechanism of deep learning using advanced mathematics. In particular, it emphasizes how to use TensorFlow and the latest MATLAB deep-learning toolboxes for implementing deep learning algorithms. As a prerequisite, readers should have a solid understanding especially of mathematical analysis, linear algebra, numerical analysis, optimizations, differential geometry, manifold, and information theory, as well as basic algebra, functional analysis, and graphical models. This computational knowledge will assist in comprehending the subject matter not only of this text/reference, but also in relevant deep learning journal articles and conference papers. This textbook/guide is aimed at Computer Science research students and engineers, as well as scientists interested in deep learning for theoretic research and analysis. More generally, this book is also helpful for those researchers who are interested in machine intelligence, pattern analysis, natural language processing, and machine vision. Dr. Wei Qi Yan is an Associate Professor in the Department of Computer Science at Auckland University of Technology, New Zealand. His other publications include the Springer title, Visual Cryptography for Image Processing and Security.

Theoretical Numerical Analysis

Theoretical Numerical Analysis Book
Author : Kendall Atkinson,Weimin Han
Publisher : Springer Science & Business Media
Release : 2007-06-07
ISBN : 0387287698
Language : En, Es, Fr & De

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Book Description :

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scienti?c disciplines and a resurgence of interest in the modern as well as the cl- sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). Thedevelopmentofnewcoursesisanaturalconsequenceofahighlevelof excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Ma- ematical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs.

Computational Methods for Precision Oncology

Computational Methods for Precision Oncology Book
Author : Alessandro Laganà
Publisher : Springer Nature
Release : 2022-03-01
ISBN : 303091836X
Language : En, Es, Fr & De

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Book Description :

Precision medicine holds great promise for the treatment of cancer and represents a unique opportunity for accelerated development and application of novel and repurposed therapeutic approaches. Current studies and clinical trials demonstrate the benefits of genomic profiling for patients whose cancer is driven by specific, targetable alterations. However, precision oncologists continue to be challenged by the widespread heterogeneity of cancer genomes and drug responses in designing personalized treatments. Chapters provide a comprehensive overview of the computational approaches, methods, and tools that enable precision oncology, as well as related biological concepts. Covered topics include genome sequencing, the architecture of a precision oncology workflow, and introduces cutting-edge research topics in the field of precision oncology. This book is intended for computational biologists, bioinformaticians, biostatisticians and computational pathologists working in precision oncology and related fields, including cancer genomics, systems biology, and immuno-oncology.

An Introduction to Functional Analysis in Computational Mathematics

An Introduction to Functional Analysis in Computational Mathematics Book
Author : V.I. Lebedev
Publisher : Birkhäuser
Release : 1996-12-01
ISBN : 9780817638887
Language : En, Es, Fr & De

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Book Description :

The book contains the methods and bases of functional analysis that are directly adjacent to the problems of numerical mathematics and its applications; they are what one needs for the understand ing from a general viewpoint of ideas and methods of computational mathematics and of optimization problems for numerical algorithms. Functional analysis in mathematics is now just the small visible part of the iceberg. Its relief and summit were formed under the influence of this author's personal experience and tastes. This edition in English contains some additions and changes as compared to the second edition in Russian; discovered errors and misprints had been corrected again here; to the author's distress, they jump incomprehensibly from one edition to another as fleas. The list of literature is far from being complete; just a number of textbooks and monographs published in Russian have been included. The author is grateful to S. Gerasimova for her help and patience in the complex process of typing the mathematical manuscript while the author corrected, rearranged, supplemented, simplified, general ized, and improved as it seemed to him the book's contents. The author thanks G. Kontarev for the difficult job of translation and V. Klyachin for the excellent figures.