Computational functional analysis:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Chichester u.a.
Horwood u.a.
2007
|
| Ausgabe: | 2. ed. |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025744016&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XII, 180 S. |
| ISBN: | 9781904275244 |
Internformat
MARC
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| 650 | 4 | |a Analyse numérique | |
| 650 | 4 | |a Différentielle Fréchet | |
| 650 | 4 | |a Différentielle Gâteaux | |
| 650 | 4 | |a Equation opérationnelle | |
| 650 | 4 | |a Espace Hilbert | |
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Datensatz im Suchindex
| _version_ | 1820966041184894976 |
|---|---|
| adam_text |
Titel: Computational functional analysis
Autor: Moore, Ramon E
Jahr: 2007
COMPUTATIONAL FUNCTIONAL
ANALYSIS
Second Edition
Ramon E. Moore
Professor of Computer and Information Science
Ohio State University
Michael J. Cloud
Associate Professor of Electrical and Computer Engineering
Lawrence Technological University, Michigan
Horwood Publishing
Chichester, UK
Table of Contents
Preface vii
Notation ix
Chapter 1 Introduction 1
Chapter 2 Linear Spaces 3
linear manifolds; isomorphic spaces; Cartesian products; equivalence
classes; factor spaces
Chapter 3 Topological Spaces 7
convergent sequences; compactness; relative compactness; sequen-
tial compactness; continuous functions; inverse mappings; homeomor-
phisms
Chapter 4 Metrie Spaces 11
metrics; isometries; Cauchy sequences; completeness; dense subsets;
separable metric spaces; completion of a metric space
Chapter 5 Normed Linear Spaces and Banach Spaces 15
norms; bounded subsets; Banach spaces; subspaces
Chapter 6 Inner Product Spaces and Hubert Spaces 19
Inner products; Cauchy-Schwarz inequality; orthogonality; E" and h;
Hubert Spaces; ££^\a,\)\ and h\ unit vectors; orthonormal sequences;
complete orthonormal sequences; separable Hubert spaces; span of a
subset; orthogonal projections; orthogonal complements; orthonormal
bases; Parseval's identity and relation; Fourier coefficients; the Gram-
Schmidt process
VI Table of Contents
Chapter 7 Linear Functionals 28
functionals; linear functionals; bounded linear functionals; evaluation
functionals; finite sums; definite integrals; inner products; the Riesz
representation theorem; null Spaces; norms; the Hahn-Banach theo-
rem; unbounded functionals; conjugate (dual) Spaces
Chapter 8 Types of Convergence in Function Spaces 32
strong convergence; weak convergence; pointwise convergence; uni-
form convergence; star convergence; weak-star convergence
Chapter 9 Reproducing Kernel Hubert Spaces 35
reproducing kerneis; orthogonal projection; interpolation; approximate
integration
Chapter 10 Order Relations in Function Spaces 42
reflexive partial orderings; intervals; interval valued mappings into
reflexively partially ordered sets; lattices; complete lattices; order
convergence; united extensions; subset property of arbitrary map-
pings; the Knaster-Tarski theorem; fixed points of arbitrary map-
pings; line segments in linear spaces; convex sets; convex mappings
Chapter 11 Operators in Function Spaces 49
Operators; linear Operators; nonlinear Operators; null spaces; non-
singular linear Operators; continuous linear Operators; bounded lin-
ear Operators; Neumann series and Solution of certain linear Opera-
tor equations; adjoint Operators; selfadjoint Operators; matrix repre-
sentations of bounded linear Operators on separable Hubert spaces;
the space L(H,H) of bounded linear Operators; types of convergence
in L(H,H); Jacobi iteration and Picard iteration; linear initial value
Problems
Chapter 12 Completely Continuous (Compact) Operators 60
completely continuous Operators; Hilbeit-Schmidt integral Operators;
projection Operators into finite dimensional subspaces; spectral the-
ory of completely continuous Operators; eigenfunction expansions;
Galerkin's method; completely continuous Operators in Banach spaces;
the Fredholm alternative
er 13 Approximation Methods for Linear Operator Equations . 68
Table of Contents vn
finite basis methods; finite difference methods; Separation of vari-
ables and eigenfunction expansions for the diffusion equation; rates
of convergence; Galerkin's method in Hubert spaces; collocation
methods; finite difference methods; Fredholm integral equations; the
Nyström method
Chapter 14 Interval Methods for Operator Equations 83
interval arithmetic; interval Integration; interval Operators; inclusion
isotonicity; nonlinear Operator equations with data perturbations
Chapter 15 Contraction Mappings and Iterative Methods 94
fixed point problems; contraction mappings; initial value problems;
two-point boundary value problems
Chapter 16 Frechet Derivatives 102
Frechet differentiable Operators; locally linear Operators; the Frechet
derivative; the Gäteaux derivative; higher Frechet derivatives; the
Taylor theorem in Banach spaces
Chapter 17 Newton's Method in Banach Spaces 116
Newton's iterative method for nonlinear Operator equations; local
convergence; the error squaring property; the Kantorovich theorem;
computational verification of convergence conditions using interval
analysis; interval versions of Newton's method
Chapter 18 Variants of Newton's Method 131
a general theorem; Ostrowski's theorem; Newton's method; the sim-
plified Newton method; the SOR-Newton method (generalized New-
ton method); a Gauss-Seidel modification
Chapter 19 Homotopy and Continuation Methods 138
homotopies; successive perturbation methods; continuation methods;
curve of zeros; discrete continuation; Davidenko's method; compu-
tational aspects
Chapter 20 A Hybrid Method for a Free Boundary Problem 146
Hints for Selected Exercises 160
Further Reading 173
Index 177 |
| any_adam_object | 1 |
| author | Moore, Ramon E. 1929-2015 Cloud, Michael J. 1960- |
| author_GND | (DE-588)108802817 (DE-588)120264242 |
| author_facet | Moore, Ramon E. 1929-2015 Cloud, Michael J. 1960- |
| author_role | aut aut |
| author_sort | Moore, Ramon E. 1929-2015 |
| author_variant | r e m re rem m j c mj mjc |
| building | Verbundindex |
| bvnumber | BV040765524 |
| callnumber-first | Q - Science |
| callnumber-label | QA320 |
| callnumber-raw | QA320 |
| callnumber-search | QA320 |
| callnumber-sort | QA 3320 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 920 |
| classification_tum | MAT 676f |
| ctrlnum | (OCoLC)255363971 (DE-599)BVBBV040765524 |
| dewey-full | 515.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7 |
| dewey-search | 515.7 |
| dewey-sort | 3515.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV040765524 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-11T15:15:44Z |
| institution | BVB |
| isbn | 9781904275244 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025744016 |
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| physical | XII, 180 S. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
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| publisher | Horwood u.a. |
| record_format | marc |
| spelling | Moore, Ramon E. 1929-2015 Verfasser (DE-588)108802817 aut Computational functional analysis Ramon E. Moore ; Michael J. Cloud 2. ed. Chichester u.a. Horwood u.a. 2007 XII, 180 S. txt rdacontent n rdamedia nc rdacarrier Analyse fonctionnelle Analyse fonctionnelle ram Analyse numérique Différentielle Fréchet Différentielle Gâteaux Equation opérationnelle Espace Hilbert Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Operatorgleichung (DE-588)4043601-9 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Operatorgleichung (DE-588)4043601-9 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Funktionalanalysis (DE-588)4018916-8 s 1\p DE-604 Cloud, Michael J. 1960- Verfasser (DE-588)120264242 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025744016&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Moore, Ramon E. 1929-2015 Cloud, Michael J. 1960- Computational functional analysis Analyse fonctionnelle Analyse fonctionnelle ram Analyse numérique Différentielle Fréchet Différentielle Gâteaux Equation opérationnelle Espace Hilbert Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd Operatorgleichung (DE-588)4043601-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4018916-8 (DE-588)4043601-9 (DE-588)4128130-5 |
| title | Computational functional analysis |
| title_auth | Computational functional analysis |
| title_exact_search | Computational functional analysis |
| title_full | Computational functional analysis Ramon E. Moore ; Michael J. Cloud |
| title_fullStr | Computational functional analysis Ramon E. Moore ; Michael J. Cloud |
| title_full_unstemmed | Computational functional analysis Ramon E. Moore ; Michael J. Cloud |
| title_short | Computational functional analysis |
| title_sort | computational functional analysis |
| topic | Analyse fonctionnelle Analyse fonctionnelle ram Analyse numérique Différentielle Fréchet Différentielle Gâteaux Equation opérationnelle Espace Hilbert Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd Operatorgleichung (DE-588)4043601-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Analyse fonctionnelle Analyse numérique Différentielle Fréchet Différentielle Gâteaux Equation opérationnelle Espace Hilbert Functional analysis Funktionalanalysis Operatorgleichung Numerisches Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025744016&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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