Theory of linear ill posed problems and its applications:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Utrecht ; Boston ; Köln ; Tokyo
VSP
2002
|
| Edition: | 1. publ. |
| Series: | Inverse and ill posed problems series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 243 - 264. - Aus dem Russ. übers. |
| Physical Description: | XIII, 281 S. 25 cm |
| ISBN: | 906764367X |
Staff View
MARC
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| 100 | 1 | |a Ivanov, Valentin K. |d 1908-1992 |e Verfasser |0 (DE-588)124630901 |4 aut | |
| 245 | 1 | 0 | |a Theory of linear ill posed problems and its applications |c V. K. Ivanov, V. V. Vasin and V. P. Tanana |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Utrecht ; Boston ; Köln ; Tokyo |b VSP |c 2002 | |
| 300 | |a XIII, 281 S. |b 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Inverse and ill posed problems series | |
| 500 | |a Literaturverz. S. 243 - 264. - Aus dem Russ. übers. | ||
| 650 | 4 | |a Integral operators | |
| 650 | 4 | |a Numerical analysis |x Improperly posed problems | |
| 650 | 4 | |a Operator equations | |
| 650 | 0 | 7 | |a Inkorrekt gestelltes Problem |0 (DE-588)4186951-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Inkorrekt gestelltes Problem |0 (DE-588)4186951-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Vasin, Vladimir V. |e Verfasser |0 (DE-588)12463091X |4 aut | |
| 700 | 1 | |a Tanana, Vitalij Pavlovič |e Verfasser |0 (DE-588)124630928 |4 aut | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009981970&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-009981970 | |
Record in the Search Index
| _version_ | 1808045484983451648 |
|---|---|
| adam_text |
CONTENTS
INTRODUCTION
1
CHAPTER
1.
WELL-POSEDNESS
OF
PROBLEMS
5
1.1.
PROBLEM
FORMULATION.
HADAMARD
'
S
CONCEPT
OF
WELL-POSEDNESS
.
5
1.2.
EXAMPLES
OF
ILL-POSED
PROBLEMS
.
8
1.3.
TIKHONOV
'
S
CONCEPT
OF
WELL-POSEDNESS.
SETS
OF
WELL-POSEDNESS
.
16
1.4.
STABILITY
THEOREMS
AND
THEIR
APPLICATIONS
.
17
1.5.
NORMAL
SOLVABILITY
OF
OPERATOR
EQUATIONS
.
25
1.6.
QUASISOLUTIONS
ON
COMPACT
AND
BOUNDEDLY
COMPACT
SETS
.
35
CHAPTER
2.
REGULARIZING
FAMILY
OF
OPERATORS
47
2.1.
POINTWISE
AND
UNIFORM
REGULARIZATION
OF
OPERATOR
EQUATIONS
.
47
2.2.
GEOMETRIC
THEOREMS
ON
STRUCTURE
OF
BOUNDEDLY
COMPACT
SETS
.
56
2.3.
UNIFORM
REGULARIZATION
OF
EQUATIONS
WITH
COMPLETELY
CONTINUOUS
OPERATORS
.
59
2.4.
STRUCTURE
OF
SETS
OF
UNIFORM
REGULARIZATION
IN
HILBERT
SPACES
.
63
2.5.
SETS
OF
UNIFORM
REGULARIZATION
FOR
CONTINUOUS
OPERATORS
.
66
CHAPTER
3.
BASIC
TECHNIQUES
FOR
CONSTRUCTING
REGULARIZING
AL
GORITHMS
71
3.1.
REDUCTION
TO
OPERATOR
EQUATIONS
OF
THE
SECOND
KIND
.
71
3.2.
METHOD
OF
QUASISOLUTIONS
.
78
3.3.
TIKHONOV
'
S
METHOD
OF
REGULARIZATION
.
83
3.4.
METHOD
OF
RESIDUAL
.
90
3.5.
ON
RELATIONS
BETWEEN
VARIATIONAL
METHODS
.
93
XII
V.
K.
IVANOV,
V.
V.
VASIN,
AND
V.
P.
TANANA
3.6.
GENERALIZED
METHOD
OF
RESIDUAL
.
99
3.7.
METHOD
BASED
ON
THE
PICARD
THEOREM
.
104
3.8.
ITERATIVE
METHODS
.
110
3.9.
REGULARIZATION
OF
THE
FREDHOLM
INTEGRAL
EQUATIONS
OF
THE
FIRST
KIND
114
3.10.
REGULARIZATION
METHODS
FOR
DIFFERENTIAL
EQUATIONS
.
127
CHAPTER
4.
OPTIMALITY
AND
STABILITY
OF
METHODS
FOR
SOLVING
ILL-POSED
PROBLEMS.
ERROR
ESTIMATION
135
4.1.
CLASSIFICATION
OF
ILL-POSED
PROBLEMS
AND
THE
CONCEPT
OF
AN
OPTIMAL
METHOD
.
135
4.2.
LOWER
ESTIMATE
FOR
ERROR
OF
THE
OPTIMAL
METHOD
.
137
4.3.
ERROR
OF
THE
REGULARIZATION
METHOD
.
142
4.4.
ALGORITHMIC
PECULIARITIES
OF
THE
GENERALIZED
METHOD
OF
RESIDUAL
.
.
150
4.5.
ERROR
OF
THE
QUASISOLUTION
METHOD
.
160
4.6.
THE
REGULARIZATION
METHOD
WITH
THE
PARAMETER
A
SATISFYING
THE
RESIDUAL
PRINCIPLE
.
164
4.7.
INVESTIGATION
OF
THE
SIMPLEST
SCHEME
OF
THE
LAVRENT
'
EV
METHOD
.
.
169
4.8.
THE
METHOD
OF
PROJECTIVE
REGULARIZATION
.
174
4.9.
CALCULATION
OF
THE
MODULE
OF
CONTINUITY
.
176
CHAPTER
5.
DETERMINATION
OF
VALUES
OF
UNBOUNDED
OPERATORS
185
5.1.
A
UNIFIED
APPROACH
TO
THE
SOLUTION
OF
ILL-POSED
PROBLEMS
.
185
5.2.
MULTIVALUED
LINEAR
OPERATORS
AND
THEIR
PROPERTIES
.
187
5.3.
DETERMINATION
OF
NORMAL
VALUES
OF
LINEAR
OPERATORS
BY
VARIATIONAL
METHODS
.
190
5.4.
THE
BEST
APPROXIMATION
OF
UNBOUNDED
OPERATORS
.
196
5.5.
OPTIMAL
REGULARIZATION
OF
THE
PROBLEM
OF
EVALUATING
A
DERIVATIVE
IN
THE
SPACE
C'(
-
OO,
OO)
.
203
CHAPTER
6.
FINITE-DIMENSIONAL
APPROXIMATION
OF
REGULIRIZING
ALGORITHMS
213
6.1.
THE
CONCEPT
OF
R-UNIFORM
CONVERGENCE
OF
LINEAR
OPERATORS
.
213
6.2.
A
GENERAL
SCHEME
OF
THE
FINITE-DIMENSIONAL
APPROXIMATION
.
217
6.3.
APPLICATION
OF
THE
GENERAL
SCHEME
.
222
6.4.
PROJECTION
METHOD
.
225
6.5.
NECESSARY
AND
SUFFICIENT
CONDITIONS
FOR
CONVERGENCE
OF
THE
PROJEC
TION
METHOD
.
228
CONTENTS
XIII
6.6.
ERROR
ESTIMATION
.
232
6.7.
NUMERICAL
APPLICATIONS
.
234
BIBLIOGRAPHY
243
ADDITIONAL
BIBLIOGRAPHY
TO
THE
SECOND
EDITION
259
COMMENTS
TO
ADDITIONAL
BIBLIOGRAPHY
265
INDEX
279 |
| any_adam_object | 1 |
| author | Ivanov, Valentin K. 1908-1992 Vasin, Vladimir V. Tanana, Vitalij Pavlovič |
| author_GND | (DE-588)124630901 (DE-588)12463091X (DE-588)124630928 |
| author_facet | Ivanov, Valentin K. 1908-1992 Vasin, Vladimir V. Tanana, Vitalij Pavlovič |
| author_role | aut aut aut |
| author_sort | Ivanov, Valentin K. 1908-1992 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 540 |
| ctrlnum | (OCoLC)50780514 (DE-599)BVBBV014729681 |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV014729681 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-22T00:28:59Z |
| institution | BVB |
| isbn | 906764367X |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009981970 |
| oclc_num | 50780514 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | XIII, 281 S. 25 cm |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | VSP |
| record_format | marc |
| series2 | Inverse and ill posed problems series |
| spelling | Ivanov, Valentin K. 1908-1992 Verfasser (DE-588)124630901 aut Theory of linear ill posed problems and its applications V. K. Ivanov, V. V. Vasin and V. P. Tanana 1. publ. Utrecht ; Boston ; Köln ; Tokyo VSP 2002 XIII, 281 S. 25 cm txt rdacontent n rdamedia nc rdacarrier Inverse and ill posed problems series Literaturverz. S. 243 - 264. - Aus dem Russ. übers. Integral operators Numerical analysis Improperly posed problems Operator equations Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd rswk-swf Inkorrekt gestelltes Problem (DE-588)4186951-5 s DE-604 Vasin, Vladimir V. Verfasser (DE-588)12463091X aut Tanana, Vitalij Pavlovič Verfasser (DE-588)124630928 aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009981970&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ivanov, Valentin K. 1908-1992 Vasin, Vladimir V. Tanana, Vitalij Pavlovič Theory of linear ill posed problems and its applications Integral operators Numerical analysis Improperly posed problems Operator equations Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd |
| subject_GND | (DE-588)4186951-5 |
| title | Theory of linear ill posed problems and its applications |
| title_auth | Theory of linear ill posed problems and its applications |
| title_exact_search | Theory of linear ill posed problems and its applications |
| title_full | Theory of linear ill posed problems and its applications V. K. Ivanov, V. V. Vasin and V. P. Tanana |
| title_fullStr | Theory of linear ill posed problems and its applications V. K. Ivanov, V. V. Vasin and V. P. Tanana |
| title_full_unstemmed | Theory of linear ill posed problems and its applications V. K. Ivanov, V. V. Vasin and V. P. Tanana |
| title_short | Theory of linear ill posed problems and its applications |
| title_sort | theory of linear ill posed problems and its applications |
| topic | Integral operators Numerical analysis Improperly posed problems Operator equations Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd |
| topic_facet | Integral operators Numerical analysis Improperly posed problems Operator equations Inkorrekt gestelltes Problem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009981970&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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