Best Approximation By Linear Superpositions Approximate Nomography
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Best Approximation By Linear Superpositions Approximate Nomography
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Author : S. I͡A. Khavinson
language : en
Publisher: American Mathematical Soc.
Release Date : 1997-01-01
Best Approximation By Linear Superpositions Approximate Nomography written by S. I͡A. Khavinson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-01 with Mathematics categories.
This book deals with problems of approximation of continuous or bounded functions of several variables by linear superposition of functions that are from the same class and have fewer variables. The main topic is the space of linear superpositions $D$ considered as a subspace of the space of continuous functions $C(X)$ on a compact space $X$. Such properties as density of $D$ in $C(X)$, its closedness, proximality, etc. are studied in great detail. The approach to these and other problems based on duality and the Hahn-Banach theorem is emphasized. Also, considerable attention is given to the discussion of the Diliberto-Straus algorithm for finding the best approximation of a given function by linear superpositions.
Best Approximation By Linear Superpositions Approximate Nomography
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FREE 30 Days
Author : S. I͡A. Khavinson
language : en
Publisher: American Mathematical Soc.
Release Date : 1997-01-01
Best Approximation By Linear Superpositions Approximate Nomography written by S. I͡A. Khavinson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-01 with Mathematics categories.
This book deals with problems of approximation of continuous or bounded functions of several variables by linear superposition of functions that are from the same class and have fewer variables. The main topic is the space of linear superpositions D considered as a sub-space of the space of continous functions C(X) on a compact space X. Such properties as density of D in C(X), its closedness, proximality, etc. are studied in great detail. The approach to these and other problems based on duality and the Hahn-Banach theorem is emphasized. Also, considerable attention is given to the discussion of the Diliberto-Straus algorithm for finding the best approximation of a given function by linear superpositions.
Ridge Functions And Applications In Neural Networks
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Author : Vugar E. Ismailov
language : en
Publisher: American Mathematical Society
Release Date : 2021-12-17
Ridge Functions And Applications In Neural Networks written by Vugar E. Ismailov and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-17 with Mathematics categories.
Recent years have witnessed a growth of interest in the special functions called ridge functions. These functions appear in various fields and under various guises. They appear in partial differential equations (where they are called plane waves), in computerized tomography, and in statistics. Ridge functions are also the underpinnings of many central models in neural network theory. In this book various approximation theoretic properties of ridge functions are described. This book also describes properties of generalized ridge functions, and their relation to linear superpositions and Kolmogorov's famous superposition theorem. In the final part of the book, a single and two hidden layer neural networks are discussed. The results obtained in this part are based on properties of ordinary and generalized ridge functions. Novel aspects of the universal approximation property of feedforward neural networks are revealed. This book will be of interest to advanced graduate students and researchers working in functional analysis, approximation theory, and the theory of real functions, and will be of particular interest to those wishing to learn more about neural network theory and applications and other areas where ridge functions are used.
Selected Topics In Complex Analysis
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Author : Vladimir Ya. Eiderman
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Selected Topics In Complex Analysis written by Vladimir Ya. Eiderman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-30 with Mathematics categories.
This volume opens with a paper by V.P. Havin that presents a comprehensive survey of the work of mathematician S.Ya. Khavinson. It includes a complete bibliography, previously unpublished, of 163 items, and twelve peer-reviewed research and expository papers by leading mathematicians, including the joint paper by Khavinson and T.S. Kuzina. The emphasis is on the usage of tools from functional analysis, potential theory, algebra, and topology.
Ridge Functions
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Author : Allan Pinkus
language : en
Publisher: Cambridge University Press
Release Date : 2015-08-07
Ridge Functions written by Allan Pinkus and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-07 with Computers categories.
Presents the state of the art in the theory of ridge functions, providing a solid theoretical foundation.
Linear Holomorphic Partial Differential Equations And Classical Potential Theory
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Author : Dmitry Khavinson
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-07-09
Linear Holomorphic Partial Differential Equations And Classical Potential Theory written by Dmitry Khavinson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-09 with Differential equations, Linear categories.
Why do solutions of linear analytic PDE suddenly break down? What is the source of these mysterious singularities, and how do they propagate? Is there a mean value property for harmonic functions in ellipsoids similar to that for balls? Is there a reflection principle for harmonic functions in higher dimensions similar to the Schwarz reflection principle in the plane? How far outside of their natural domains can solutions of the Dirichlet problem be extended? Where do the continued solutions become singular and why? This book invites graduate students and young analysts to explore these and many other intriguing questions that lead to beautiful results illustrating a nice interplay between parts of modern analysis and themes in “physical” mathematics of the nineteenth century. To make the book accessible to a wide audience including students, the authors do not assume expertise in the theory of holomorphic PDE, and most of the book is accessible to anyone familiar with multivariable calculus and some basics in complex analysis and differential equations.
Sign Based Methods In Linear Statistical Models
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Author : M. V. Boldin
language : en
Publisher: American Mathematical Soc.
Release Date : 1997-04-22
Sign Based Methods In Linear Statistical Models written by M. V. Boldin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-04-22 with Mathematics categories.
For nonparametric statistics, the last half of this century was the time when rank-based methods originated, were vigorously developed, reached maturity, and received wide recognition. The rank-based approach in statistics consists in ranking the observed values and using only the ranks rather than the original numerical data. In fitting relationships to observed data, the ranks of residuals from the fitted dependence are used. The signed-based approach is based on the assumption that random errors take positive or negative values with equal probabilities. Under this assumption, the sign procedures are distribution-free. These procedures are robust to violations of model assumptions, for instance, to even a considerable number of gross errors in observations. In addition, sign procedures have fairly high relative asymptotic efficiency, in spite of the obvious loss of information incurred by the use of signs instead of the corresponding numerical values. In this work, sign-based methods in the framework of linear models are developed. In the first part of the book, there are linear and factor models involving independent observations. In the second part, linear models of time series, primarily autoregressive models, are considered.
Linear And Nonlinear Perturbations Of The Operator Div
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Author : Viktor Grigorʹevich Osmolovskiĭ
language : en
Publisher: American Mathematical Soc.
Release Date : 1997-01-01
Linear And Nonlinear Perturbations Of The Operator Div written by Viktor Grigorʹevich Osmolovskiĭ and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-01 with Mathematics categories.
This book presents results onboundary-value problems for L and the theory of nonlinear perturbations of L. Specifically, necessary and sufficient solvability conditions in explicit form are found for various boundary-value problems for the operator L. an analog of the Weyl decomposition is proved.
Ordinary Differential Equations With Constant Coefficient
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Author : Serge_ Konstantinovich Godunov
language : en
Publisher: American Mathematical Soc.
Release Date : 1997-08-19
Ordinary Differential Equations With Constant Coefficient written by Serge_ Konstantinovich Godunov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-08-19 with Mathematics categories.
This book presents the theory of ordinary differential equations with constant coefficients. The exposition is based on ideas developing the Gelfand-Shilov theorem on the polynomial representation of a matrix exponential. Boundary value problems for ordinary equations, Green matrices, Green functions, the Lopatinskii condition, and Lyapunov stability are considered. This volume can be used for practical study of ordinary differential equations using computers. In particular, algorithms and computational procedures, including the orthogonal sweep method, are described. The book also deals with stationary optimal control systems described by systems of ordinary differential equations with constant coefficients. The notions of controllability, observability, and stabilizability are analyzed, and some questions on the matrix Lure-Riccati equations are studied.
Probability Theory
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Author : Anatoli_ I_A_kovlevich Dorogovt_s_ev
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-06-21
Probability Theory written by Anatoli_ I_A_kovlevich Dorogovt_s_ev and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-21 with Mathematics categories.
This book of problems is intended for students in pure and applied mathematics. There are problems in traditional areas of probability theory and problems in the theory of stochastic processes, which has wide applications in the theory of automatic control, queuing and reliability theories, and in many other modern science and engineering fields. Answers to most of the problems are given, and the book provides hints and solutions for more complicated problems.