Numerical methods for the solution of ill posed problems:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer
1995
|
| Schriftenreihe: | Mathematics and its applications
328 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Russ. übers. |
| Beschreibung: | IX, 253 S. graph. Darst. |
| ISBN: | 079233583X |
Internformat
MARC
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| 245 | 1 | 0 | |a Numerical methods for the solution of ill posed problems |c by A. N. Tikhonov ... |
| 246 | 1 | 3 | |a Numerical methods for the solution of ill-posed problems |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1995 | |
| 300 | |a IX, 253 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 328 | |
| 500 | |a Aus dem Russ. übers. | ||
| 650 | 0 | 7 | |a Inkorrekt gestelltes Problem |0 (DE-588)4186951-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Inkorrekt gestelltes Problem |0 (DE-588)4186951-5 |D s |
| 689 | 0 | 1 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Tichonov, Andrej N. |e Sonstige |4 oth | |
| 830 | 0 | |a Mathematics and its applications |v 328 |w (DE-604)BV008163334 |9 328 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006907843&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1804124800261554176 |
|---|---|
| adam_text | Contents
Preface to the English edition ix
Introduction 1
Chapter 1. Regularization methods 7
1. Statement of the problem. The smoothing functional 7
2. Choice of the regularization parameter 8
3. Equivalence of the generalized discrepancy principle and the gen¬
eralized discrepancy method 16
4. The generalized discrepancy and its properties 19
5. Finite dimensional approximation of ill posed problems 28
6. Numerical methods for solving certain problems of linear algebra 32
7. Equations of convolution type 34
8. Nonlinear ill posed problems 45
9. Incompatible ill posed problems 52
Chapter 2. Numerical methods for the approximate solution of ill posed
problems on compact sets 65
1. Approximate solution of ill posed problems on compact sets 66
2. Some theorems regarding uniform approximation to the exact so¬
lution of ill posed problems 67
3. Some theorems about convex polyhedra in Rn 70
4. The solution of ill posed problems on sets of convex functions 75
5. Uniform convergence of approximate solutions of bounded varia¬
tion 76
V
vi CONTENTS
Chapter 3. Algorithms for the approximate solution of ill posed prob¬
lems on special sets 81
1. Application of the conditional gradient method for solving problems
on special sets 81
2. Application of the method of projection of conjugate gradients to
the solution of ill posed problems on sets of special structure 88
3. Application of the method of projection of conjugate gradients, with
projection into the set of vectors with nonnegative components, to the
solution of ill posed problems on sets of special structure 92
Chapter 4. Algorithms and programs for solving linear ill posed prob¬
lems 97
0.1. Some general programs 98
1. Description of the program for solving ill posed problems by the
regularization method 100
1.1. Description of the program PTIMR 102
1.2. Description of the program PTIZR 110
2. Description of the program for solving integral equations with a
priori constraints by the regularization method 116
2.1. Description of the program PTIPR 116
3. Description of the program for solving integral equations of convo¬
lution type 122
3.1. Description of the program PTIKR 123
4. Description of the program for solving two dimensional integral
equations of convolution type 131
5. Description of the program for solving ill posed problems on special
sets. The method of the conditional gradient 139
5.1. Description of the program PTIGR 139
5.2. Description of the program PTIGR1 141
5.3. Description of the program PTIGR2 142
6. Description of the program for solving ill posed problems on special
sets. The method of projection of conjugate gradients 146
6.1. Description of the program PTILR 146
6.2. Description of the program PTILR1 147
7. Description of the program for solving ill posed problems on special
sets. The method of conjugate gradients with projection into the set of
vectors with nonnegative components 153
7.1. Description of the program PTISR 153
7.2. Description of the program PTISR1 155
CONTENTS vii
Appendix: Program listings 163
I. Program for solving Predholm integral equations of the first kind,
using Tikhonov s method with transformation of the Euler equation to
tridiagonal form 163
II. Program for solving Fredholm integral equations of the first kind
by Tikhonov s method, using the conjugate gradient method 177
III. Program for solving Predholm integral equations of the first kind
on the set of nonnegative functions, using the regularization method 183
IV. Program for solving one dimensional integral equations of convo¬
lution type 188
V. Program for solving two dimensional integral equations of convolu¬
tion type 196
VI. Program for solving Fredholm integral equations of the first kind
on the sets of monotone and (or) convex functions. The method of the
conditional gradient 204
VII. Program for solving Fredholm integral equations of the first kind
on the sets of monotone and (or) convex functions. The method of
projection of conjugate gradients 209
VIII. Program for solving Fredholm integral equations of the first kind
on the sets of monotone and (or) convex functions. The method of pro¬
jection of conjugate gradients onto the set of vectors with nonnegative
coordinates 221
IX. General programs 229
Postscript 235
1. Variational methods 235
2. Iterative methods 236
3. Statistical methods 237
4. Textbooks 237
5. Handbooks and Conference Proceedings 238
|
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| dewey-raw | 519.4 |
| dewey-search | 519.4 |
| dewey-sort | 3519.4 |
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| id | DE-604.BV010375990 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:51:25Z |
| institution | BVB |
| isbn | 079233583X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006907843 |
| oclc_num | 832679301 |
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| owner_facet | DE-12 DE-91 DE-BY-TUM DE-20 DE-703 DE-355 DE-BY-UBR DE-83 DE-11 DE-188 |
| physical | IX, 253 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Numerical methods for the solution of ill posed problems by A. N. Tikhonov ... Numerical methods for the solution of ill-posed problems Dordrecht [u.a.] Kluwer 1995 IX, 253 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 328 Aus dem Russ. übers. Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Inkorrekt gestelltes Problem (DE-588)4186951-5 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Tichonov, Andrej N. Sonstige oth Mathematics and its applications 328 (DE-604)BV008163334 328 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006907843&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Numerical methods for the solution of ill posed problems Mathematics and its applications Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4186951-5 (DE-588)4128130-5 |
| title | Numerical methods for the solution of ill posed problems |
| title_alt | Numerical methods for the solution of ill-posed problems |
| title_auth | Numerical methods for the solution of ill posed problems |
| title_exact_search | Numerical methods for the solution of ill posed problems |
| title_full | Numerical methods for the solution of ill posed problems by A. N. Tikhonov ... |
| title_fullStr | Numerical methods for the solution of ill posed problems by A. N. Tikhonov ... |
| title_full_unstemmed | Numerical methods for the solution of ill posed problems by A. N. Tikhonov ... |
| title_short | Numerical methods for the solution of ill posed problems |
| title_sort | numerical methods for the solution of ill posed problems |
| topic | Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Inkorrekt gestelltes Problem Numerisches Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006907843&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT tichonovandrejn numericalmethodsforthesolutionofillposedproblems |