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The Resource An Introduction to Functional Analysis in Computational Mathematics : An Introduction, by V.I. Lebedev, (electronic resource)
An Introduction to Functional Analysis in Computational Mathematics : An Introduction, by V.I. Lebedev, (electronic resource)
Resource Information
The item An Introduction to Functional Analysis in Computational Mathematics : An Introduction, by V.I. Lebedev, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item An Introduction to Functional Analysis in Computational Mathematics : An Introduction, by V.I. Lebedev, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 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
 Language

 eng
 eng
 Edition
 1st ed. 1997.
 Extent
 1 online resource (XII, 256 p.)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 Contents

 1. Functional Spaces and Problems in the Theory of Approximation
 1. Metric Spaces
 2. Compact Sets in Metric Spaces
 3. Statement of the Main Extremal Problems in the Theory of Approximation. Main Characteristics of the Best Approximations
 4. The Contraction Mapping Principle
 5. Linear Spaces
 6. Normed and Banach Spaces
 7. Spaces with an Inner Product. Hilbert Spaces
 8. Problems on the Best Approximation. Orthogonal Expansions and Fourier Series in a Hilbert Space
 9. Some Extremal Problems in Normed and Hilbert Spaces
 10. Polynomials the Least Deviating from Zero. Chebyshev Polynomials and Their Properties
 11. Some Extremal Polynomials
 2. Linear Operators and Functionals
 1. Linear Operators in Banach Spaces
 2. Spaces of Linear Operators
 3. Inverse Operators. Linear Operator Equations. Condition Measure of Operator
 4. Spectrum and Spectral Radius of Operator. Convergence Conditions for the Neumann Series. Perturbations Theorem
 5. Uniform Boundedness Principle
 6. Linear Functionals and Adjoint Space
 7. The Riesz Theorem. The HahnBanach Theorem. Optimization Problem for Quadrature Formulas. The Duality Principle
 8. Adjoint, Selfadjoint, Symmetric Operators
 9. Eigenvalues and Eigenelements of Selfadjoint and Symmetric Operators
 10. Quadrature Functionals with Positive Definite Symmetric or Symmetrizable Operator and Generalized Solutions of Operator Equations
 11. Variational Methods for the Minimization of Quadrature Functionals
 12. Variational Equations. The VishikLaxMilgram Theorem
 13. Compact (Completely Continuous) Operators in Hilbert Space
 14. The Sobolev Spaces. Embedding Theorems
 15. Generalized Solution of the Dirichlet Problem for Elliptic Equations of the Second Order
 3. Iteration Methods for the Solution of Operator Equations
 1. General Theory of Iteration Methods
 2. On the Existence of Convergent Iteration Methods and Their Optimization
 3. The Chebyshev OneStep (Binomial) Iteration Methods
 4. The Chebyshev TwoStep (Trinomial) Iteration Method
 5. The Chebyshev Iteration Methods for Equations with Symmetrized Operators
 6. Block Chebyshev Method
 7. The Descent Methods
 8. Differentiation and Integration of Nonlinear Operators. The Newton Method
 9. Partial Eigenvalue Problem
 10. Successive Approximation Method for Inverse Operator
 11. Stability and Optimization of Explicit Difference Schemes for Stiff Differential Equations
 Isbn
 9781461241287
 Label
 An Introduction to Functional Analysis in Computational Mathematics : An Introduction
 Title
 An Introduction to Functional Analysis in Computational Mathematics
 Title remainder
 An Introduction
 Statement of responsibility
 by V.I. Lebedev
 Language

 eng
 eng
 Summary
 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
 http://library.link/vocab/creatorName
 Lebedev, V.I
 Dewey number
 515.7
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
 _NpBfWVAQPc
 Image bit depth
 0
 Language note
 English
 LC call number
 QA319329.9
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/subjectName

 Functional analysis
 Computer science
 Computer science
 Mathematics
 Functional Analysis
 Computational Mathematics and Numerical Analysis
 Math Applications in Computer Science
 Applications of Mathematics
 Label
 An Introduction to Functional Analysis in Computational Mathematics : An Introduction, by V.I. Lebedev, (electronic resource)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code
 cr
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Contents
 1. Functional Spaces and Problems in the Theory of Approximation  1. Metric Spaces  2. Compact Sets in Metric Spaces  3. Statement of the Main Extremal Problems in the Theory of Approximation. Main Characteristics of the Best Approximations  4. The Contraction Mapping Principle  5. Linear Spaces  6. Normed and Banach Spaces  7. Spaces with an Inner Product. Hilbert Spaces  8. Problems on the Best Approximation. Orthogonal Expansions and Fourier Series in a Hilbert Space  9. Some Extremal Problems in Normed and Hilbert Spaces  10. Polynomials the Least Deviating from Zero. Chebyshev Polynomials and Their Properties  11. Some Extremal Polynomials  2. Linear Operators and Functionals  1. Linear Operators in Banach Spaces  2. Spaces of Linear Operators  3. Inverse Operators. Linear Operator Equations. Condition Measure of Operator  4. Spectrum and Spectral Radius of Operator. Convergence Conditions for the Neumann Series. Perturbations Theorem  5. Uniform Boundedness Principle  6. Linear Functionals and Adjoint Space  7. The Riesz Theorem. The HahnBanach Theorem. Optimization Problem for Quadrature Formulas. The Duality Principle  8. Adjoint, Selfadjoint, Symmetric Operators  9. Eigenvalues and Eigenelements of Selfadjoint and Symmetric Operators  10. Quadrature Functionals with Positive Definite Symmetric or Symmetrizable Operator and Generalized Solutions of Operator Equations  11. Variational Methods for the Minimization of Quadrature Functionals  12. Variational Equations. The VishikLaxMilgram Theorem  13. Compact (Completely Continuous) Operators in Hilbert Space  14. The Sobolev Spaces. Embedding Theorems  15. Generalized Solution of the Dirichlet Problem for Elliptic Equations of the Second Order  3. Iteration Methods for the Solution of Operator Equations  1. General Theory of Iteration Methods  2. On the Existence of Convergent Iteration Methods and Their Optimization  3. The Chebyshev OneStep (Binomial) Iteration Methods  4. The Chebyshev TwoStep (Trinomial) Iteration Method  5. The Chebyshev Iteration Methods for Equations with Symmetrized Operators  6. Block Chebyshev Method  7. The Descent Methods  8. Differentiation and Integration of Nonlinear Operators. The Newton Method  9. Partial Eigenvalue Problem  10. Successive Approximation Method for Inverse Operator  11. Stability and Optimization of Explicit Difference Schemes for Stiff Differential Equations
 Dimensions
 unknown
 Edition
 1st ed. 1997.
 Extent
 1 online resource (XII, 256 p.)
 File format
 multiple file formats
 Form of item
 online
 Isbn
 9781461241287
 Level of compression
 uncompressed
 Media category
 computer
 Media type code
 c
 Other control number
 10.1007/9781461241287
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number

 (CKB)3400000000090716
 (SSID)ssj0001297212
 (PQKBManifestationID)11858105
 (PQKBTitleCode)TC0001297212
 (PQKBWorkID)11362347
 (PQKB)11187024
 (DEHe213)9781461241287
 (MiAaPQ)EBC3075971
 (EXLCZ)993400000000090716
 Label
 An Introduction to Functional Analysis in Computational Mathematics : An Introduction, by V.I. Lebedev, (electronic resource)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code
 cr
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Contents
 1. Functional Spaces and Problems in the Theory of Approximation  1. Metric Spaces  2. Compact Sets in Metric Spaces  3. Statement of the Main Extremal Problems in the Theory of Approximation. Main Characteristics of the Best Approximations  4. The Contraction Mapping Principle  5. Linear Spaces  6. Normed and Banach Spaces  7. Spaces with an Inner Product. Hilbert Spaces  8. Problems on the Best Approximation. Orthogonal Expansions and Fourier Series in a Hilbert Space  9. Some Extremal Problems in Normed and Hilbert Spaces  10. Polynomials the Least Deviating from Zero. Chebyshev Polynomials and Their Properties  11. Some Extremal Polynomials  2. Linear Operators and Functionals  1. Linear Operators in Banach Spaces  2. Spaces of Linear Operators  3. Inverse Operators. Linear Operator Equations. Condition Measure of Operator  4. Spectrum and Spectral Radius of Operator. Convergence Conditions for the Neumann Series. Perturbations Theorem  5. Uniform Boundedness Principle  6. Linear Functionals and Adjoint Space  7. The Riesz Theorem. The HahnBanach Theorem. Optimization Problem for Quadrature Formulas. The Duality Principle  8. Adjoint, Selfadjoint, Symmetric Operators  9. Eigenvalues and Eigenelements of Selfadjoint and Symmetric Operators  10. Quadrature Functionals with Positive Definite Symmetric or Symmetrizable Operator and Generalized Solutions of Operator Equations  11. Variational Methods for the Minimization of Quadrature Functionals  12. Variational Equations. The VishikLaxMilgram Theorem  13. Compact (Completely Continuous) Operators in Hilbert Space  14. The Sobolev Spaces. Embedding Theorems  15. Generalized Solution of the Dirichlet Problem for Elliptic Equations of the Second Order  3. Iteration Methods for the Solution of Operator Equations  1. General Theory of Iteration Methods  2. On the Existence of Convergent Iteration Methods and Their Optimization  3. The Chebyshev OneStep (Binomial) Iteration Methods  4. The Chebyshev TwoStep (Trinomial) Iteration Method  5. The Chebyshev Iteration Methods for Equations with Symmetrized Operators  6. Block Chebyshev Method  7. The Descent Methods  8. Differentiation and Integration of Nonlinear Operators. The Newton Method  9. Partial Eigenvalue Problem  10. Successive Approximation Method for Inverse Operator  11. Stability and Optimization of Explicit Difference Schemes for Stiff Differential Equations
 Dimensions
 unknown
 Edition
 1st ed. 1997.
 Extent
 1 online resource (XII, 256 p.)
 File format
 multiple file formats
 Form of item
 online
 Isbn
 9781461241287
 Level of compression
 uncompressed
 Media category
 computer
 Media type code
 c
 Other control number
 10.1007/9781461241287
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number

 (CKB)3400000000090716
 (SSID)ssj0001297212
 (PQKBManifestationID)11858105
 (PQKBTitleCode)TC0001297212
 (PQKBWorkID)11362347
 (PQKB)11187024
 (DEHe213)9781461241287
 (MiAaPQ)EBC3075971
 (EXLCZ)993400000000090716
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