The Resource Approximation by max-product type operators, Barnabás Bede, Lucian Coroianu, Sorin G. Gal

Approximation by max-product type operators, Barnabás Bede, Lucian Coroianu, Sorin G. Gal

Label
Approximation by max-product type operators
Title
Approximation by max-product type operators
Statement of responsibility
Barnabás Bede, Lucian Coroianu, Sorin G. Gal
Creator
Contributor
Author
Subject
Genre
Language
eng
Summary
This monograph presents a broad treatment of developments in an area of constructive approximation involving the so-called "max-product" type operators. The exposition highlights the max-product operators as those which allow one to obtain, in many cases, more valuable estimates than those obtained by classical approaches. The text considers a wide variety of operators which are studied for a number of interesting problems such as quantitative estimates, convergence, saturation results, localization, to name several. Additionally, the book discusses the perfect analogies between the probabilistic approaches of the classical Bernstein type operators and of the classical convolution operators (non-periodic and periodic cases), and the possibilistic approaches of the max-product variants of these operators. These approaches allow for two natural interpretations of the max-product Bernstein type operators and convolution type operators: firstly, as possibilistic expectations of some fuzzy variables, and secondly, as bases for the Feller type scheme in terms of the possibilistic integral. These approaches also offer new proofs for the uniform convergence based on a Chebyshev type inequality in the theory of possibility. Researchers in the fields of approximation of functions, signal theory, approximation of fuzzy numbers, image processing, and numerical analysis will find this book most beneficial. This book is also a good reference for graduates and postgraduates taking courses in approximation theory
Cataloging source
N$T
http://library.link/vocab/creatorName
Bede, Barnabas
Dewey number
511.4
Index
index present
LC call number
QA221
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1953-
http://library.link/vocab/relatedWorkOrContributorName
  • Coroianu, Lucian
  • Gal, Sorin G.
http://library.link/vocab/subjectName
  • Approximation theory
  • Operator theory
  • Constructive mathematics
  • Fuzzy mathematics
  • MATHEMATICS
  • Approximation theory
  • Constructive mathematics
  • Fuzzy mathematics
  • Operator theory
  • Functional analysis & transforms
  • Applied mathematics
  • Integral calculus & equations
  • Differential calculus & equations
Label
Approximation by max-product type operators, Barnabás Bede, Lucian Coroianu, Sorin G. Gal
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-3-319-34189-7
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Preface; Contents; 1 Introduction and Preliminaries; 1.1 Introduction; 1.1.1 Linear Approximation Operators; 1.1.2 Definitions of the Max-Product Operators; 1.1.3 Main Characteristics of the Max-Product Operators; 1.2 Preliminaries; 1.2.1 Notes on Fuzzy Numbers; 1.2.2 Notes on Possibility Theory; 2 Approximation by Max-Product Bernstein Operators; 2.1 Estimates for Positive Functions; 2.2 Improved Estimates for Strictly Positive Functions; 2.3 Saturation Results; 2.4 Localization Results; 2.5 Iterations and Fixed Points; 2.6 Applications to Approximation of Fuzzy Numbers
  • 2.6.1 Uniform Approximation and Preservation of Characteristics2.6.2 L1-Approximation; 2.7 Bivariate Max-Product Bernstein Operators; 2.8 Applications to Image Processing; 2.9 Notes; 3 Approximation by Max-Product Favard-Szász-Mirakjan Operators; 3.1 Non-Truncated Operators; 3.2 Truncated Operators; 4 Approximation by Max-Product Baskakov Operators; 4.1 Non-Truncated Operators; 4.2 Truncated Operators; 5 Approximation by Max-Product Bleimann-Butzer-Hahn Operators; 5.1 Quantitative Estimates; 5.2 Shape Preserving Properties; 6 Approximation by Max-Product Meyer-König and Zeller Operators
  • 6.1 Estimates and Shape Preserving Properties6.2 Saturation Results; 6.3 Localization Results; 6.4 Note; 7 Approximation by Max-Product Interpolation Operators; 7.1 Max-Product Hermite-Fejér Interpolation on Chebyshev Knots; 7.2 Max-Product Lagrange Interpolation on Chebyshev Knots; 7.3 Modified Max-Product Lagrange Interpolation on General Knots; 7.4 Saturation Results for Equidistant Knots; 7.5 Localization Results for Equidistant Knots; 8 Approximations by Max-Product Sampling Operators; 8.1 Max-Product Generalized Sampling Operators
  • 8.2 Max-Product Sampling Operators Based on Sinc-Type Kernels8.3 Saturation and Localization for Truncated Operators; 8.3.1 The Saturation Order for the Tn(M) Operator; 8.3.2 The Saturation Order for the Wn(M) Operator; 8.3.3 Local Inverse Result for the Tn(M) Operator; 8.3.4 Localization and Local Direct Result for the Tn(M) Operator; 8.3.5 Localization, Local Inverse, and Local Direct Results for the Wn(M) Operator; 8.4 Saturation and Localization for Non-Truncated Operators; 8.4.1 Saturation for the Case of Fejér Kernel; 8.4.2 Local Inverse Result for the Case of Fejér Kernel
  • 8.4.3 Localization Results in the Case of Fejér Kernel8.4.4 The Case of the Whittaker operator; 8.5 Notes; 9 Global Smoothness Preservation Properties; 9.1 The Case of Max-Product Bernstein operator; 9.2 The Case of Max-Product Hermite-Féjer Operator; 9.3 The Case of Max-Product Lagrange Operator; 10 Possibilistic Approaches of the Max-Product Type Operators; 10.1 Bernstein-Type Approach in Possibility Theory; 10.1.1 Max-Product Operators on C+[0, 1]; 10.1.2 Max-Product Operators on UC+[0, +∞); 10.2 Feller's Scheme in Possibility Theory
Dimensions
unknown
Extent
1 online resource
File format
unknown
Form of item
online
Isbn
9783319341897
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
SpringerLink
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)956505364
  • (OCoLC)ocn956505364
Label
Approximation by max-product type operators, Barnabás Bede, Lucian Coroianu, Sorin G. Gal
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-3-319-34189-7
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Preface; Contents; 1 Introduction and Preliminaries; 1.1 Introduction; 1.1.1 Linear Approximation Operators; 1.1.2 Definitions of the Max-Product Operators; 1.1.3 Main Characteristics of the Max-Product Operators; 1.2 Preliminaries; 1.2.1 Notes on Fuzzy Numbers; 1.2.2 Notes on Possibility Theory; 2 Approximation by Max-Product Bernstein Operators; 2.1 Estimates for Positive Functions; 2.2 Improved Estimates for Strictly Positive Functions; 2.3 Saturation Results; 2.4 Localization Results; 2.5 Iterations and Fixed Points; 2.6 Applications to Approximation of Fuzzy Numbers
  • 2.6.1 Uniform Approximation and Preservation of Characteristics2.6.2 L1-Approximation; 2.7 Bivariate Max-Product Bernstein Operators; 2.8 Applications to Image Processing; 2.9 Notes; 3 Approximation by Max-Product Favard-Szász-Mirakjan Operators; 3.1 Non-Truncated Operators; 3.2 Truncated Operators; 4 Approximation by Max-Product Baskakov Operators; 4.1 Non-Truncated Operators; 4.2 Truncated Operators; 5 Approximation by Max-Product Bleimann-Butzer-Hahn Operators; 5.1 Quantitative Estimates; 5.2 Shape Preserving Properties; 6 Approximation by Max-Product Meyer-König and Zeller Operators
  • 6.1 Estimates and Shape Preserving Properties6.2 Saturation Results; 6.3 Localization Results; 6.4 Note; 7 Approximation by Max-Product Interpolation Operators; 7.1 Max-Product Hermite-Fejér Interpolation on Chebyshev Knots; 7.2 Max-Product Lagrange Interpolation on Chebyshev Knots; 7.3 Modified Max-Product Lagrange Interpolation on General Knots; 7.4 Saturation Results for Equidistant Knots; 7.5 Localization Results for Equidistant Knots; 8 Approximations by Max-Product Sampling Operators; 8.1 Max-Product Generalized Sampling Operators
  • 8.2 Max-Product Sampling Operators Based on Sinc-Type Kernels8.3 Saturation and Localization for Truncated Operators; 8.3.1 The Saturation Order for the Tn(M) Operator; 8.3.2 The Saturation Order for the Wn(M) Operator; 8.3.3 Local Inverse Result for the Tn(M) Operator; 8.3.4 Localization and Local Direct Result for the Tn(M) Operator; 8.3.5 Localization, Local Inverse, and Local Direct Results for the Wn(M) Operator; 8.4 Saturation and Localization for Non-Truncated Operators; 8.4.1 Saturation for the Case of Fejér Kernel; 8.4.2 Local Inverse Result for the Case of Fejér Kernel
  • 8.4.3 Localization Results in the Case of Fejér Kernel8.4.4 The Case of the Whittaker operator; 8.5 Notes; 9 Global Smoothness Preservation Properties; 9.1 The Case of Max-Product Bernstein operator; 9.2 The Case of Max-Product Hermite-Féjer Operator; 9.3 The Case of Max-Product Lagrange Operator; 10 Possibilistic Approaches of the Max-Product Type Operators; 10.1 Bernstein-Type Approach in Possibility Theory; 10.1.1 Max-Product Operators on C+[0, 1]; 10.1.2 Max-Product Operators on UC+[0, +∞); 10.2 Feller's Scheme in Possibility Theory
Dimensions
unknown
Extent
1 online resource
File format
unknown
Form of item
online
Isbn
9783319341897
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
SpringerLink
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)956505364
  • (OCoLC)ocn956505364

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