Books in Approximations and expansions

Approximation Theory and Applications

1st Edition
February 4, 2025
Sergei Aliukov
English
Paperback
9 7 8 0 4 4 3 2 9 1 4 1 8
eBook
9 7 8 0 4 4 3 2 9 1 4 2 5

Approximation Theory and Applications: Piecewise Linear and Generalized Functions presents the main provisions of approximation theory, and considers existing and new methods for approximating piecewise linear and generalized functions, widely used to solve problems related to mathematical modeling of systems, processes, and phenomena in fields ranging from engineering to economics. The widespread use of piecewise linear and generalized functions is explained by the simplicity of their structure. However, challenges often arise when constructing solutions over the entire domain of these functions, requiring the use special mathematical methods to put theory into practice. This book first offers a first full foundation in approximation theory as it relates to piecewise linear and generalized functions, followed by staged methods to resolve common problems in practice, with applications examined across structural mechanics, medicine, quantum theory, signal theory, semiconductor theory, mechanical engineering, heat engineering, and other fields. Later chapters consider numerical verification of approximation methods, and approximation theory as the basis for new macroeconomic theory with impulse and jump characteristics. Each chapter includes questions for review and sample problems, accompanied by a separate Solutions Manual hosted for instructor access.

Hilbertian Kernels and Spline Functions

1st Edition
Volume 4
June 28, 2014
M. Atteia
English
eBook
9 7 8 1 4 8 3 2 9 5 1 9 0

In this monograph, which is an extensive study of Hilbertian approximation, the emphasis is placed on spline functions theory. The origin of the book was an effort to show that spline theory parallels Hilbertian Kernel theory, not only for splines derived from minimization of a quadratic functional but more generally for splines considered as piecewise functions type.Being as far as possible self-contained, the book may be used as a reference, with information about developments in linear approximation, convex optimization, mechanics and partial differential equations.

Stability by Liapunov's Direct Method with Applications by Joseph L Salle and Solomon Lefschetz

1st Edition
Volume 4
January 1, 1961
Joseph La Salle + 1 more
English
eBook
9 7 8 0 0 8 0 9 5 5 1 2 4

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.

Approximation Problems in Analysis and Probability

1st Edition
Volume 159
August 18, 2011
M.P. Heble
English
eBook
9 7 8 0 0 8 0 8 7 2 7 0 4

This is an exposition of some special results on analytic or C∞-approximation of functions in the strong sense, in finite- and infinite-dimensional spaces. It starts with H. Whitney's theorem on strong approximation by analytic functions in finite-dimensional spaces and ends with some recent results by the author on strong C∞-approximation of functions defined in a separable Hilbert space. The volume also contains some special results on approximation of stochastic processes. The results explained in the book have been obtained over a span of nearly five decades.

Computational Methods for Modeling of Nonlinear Systems by Anatoli Torokhti and Phil Howlett

1st Edition
Volume 212
March 2, 2007
Anatoli Torokhti + 1 more
English
Hardback
9 7 8 0 4 4 4 5 3 0 4 4 8
eBook
9 7 8 0 0 8 0 4 7 5 3 8 7

Topics in Multivariate Approximation and Interpolation

1st Edition
Volume 12
November 15, 2005
Kurt Jetter + 4 more
English
Hardback
9 7 8 0 4 4 4 5 1 8 4 4 6
eBook
9 7 8 0 0 8 0 4 6 2 0 4 2

This book is a collection of eleven articles, written by leading experts and dealing with special topics in Multivariate Approximation and Interpolation. The material discussed here has far-reaching applications in many areas of Applied Mathematics, such as in Computer Aided Geometric Design, in Mathematical Modelling, in Signal and Image Processing and in Machine Learning, to mention a few. The book aims at giving a comprehensive information leading the reader from the fundamental notions and results of each field to the forefront of research. It is an ideal and up-to-date introduction for graduate students specializing in these topics, and for researchers in universities and in industry.

Differential Geometry and the Calculus of Variations by Robert Hermann

1st Edition
Volume 49
April 1, 2000
Robert Hermann
English
eBook
9 7 8 0 0 8 0 9 5 5 5 7 5

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; andmethods 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 particularbranches, such as optimal filtering and information compression.

Systems and Simulation by Dimitris N Chorafas

1st Edition
Volume 14
April 1, 2000
Dimitris N. Chorafas
English
eBook
9 7 8 0 0 8 0 9 5 7 8 1 4

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; andmethods 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 particularbranches, such as optimal filtering and information compression.

Extensions of Linear-Quadratic Control, Optimization and Matrix Theory

1st Edition
Volume 133
April 1, 2000
David H. JACOBSON
English
eBook
9 7 8 0 0 8 0 9 5 6 4 2 8

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; andmethods 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 particularbranches, such as optimal filtering and information compression.

Stability of Motion by A M Liapunov

1st Edition
Volume 30
April 1, 2000
A. M. Liapunov
English
eBook
9 7 8 0 0 8 0 9 5 5 3 7 7

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; andmethods 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 particularbranches, such as optimal filtering and information compression.

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