MARC details
| 000 -LEADER |
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| fixed length control field |
03822cam a2200301 a 4500 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
100927s2011 gw a b 001 0 eng |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783110250640 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
3110250640 |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
SDU |
| 050 00 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA377 |
| Item number |
B166 I 2011 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Bakushinskiĭ, A. B. |
| 245 10 - TITLE STATEMENT |
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| Title |
Iterative methods for ill-posed problems : |
| Remainder of title |
an introduction / |
| Statement of responsibility, etc. |
Anatoly B. Bakushinsky, Mikhail Yu. Kokurin, Alexandra Smirnova. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. |
|---|
| Place of publication, distribution, etc. |
Berlin ; |
| -- |
New York : |
| Name of publisher, distributor, etc. |
De Gruyter, |
| Date of publication, distribution, etc. |
2011. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
136 p. : |
| Other physical details |
ill. |
| 490 1# - SERIES STATEMENT |
|---|
| Series Statement |
Inverse and ill-posed problems series ; |
| Volume/sequential designation |
54 |
| 505 00 - Formatted Contents Note |
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| Title |
The regularity condition. Newton's method -- |
| -- |
Preliminary results -- |
| -- |
Linearization procedure -- |
| -- |
Error analysis -- |
| -- |
Problems -- |
| -- |
The Gauss -- Newton method -- |
| -- |
Motivation -- |
| -- |
Convergence rates -- |
| -- |
Problems -- |
| -- |
The gradient method -- |
| -- |
The gradient method for regular problems -- |
| -- |
Ill-posed case -- |
| -- |
Problems -- |
| -- |
Tikhonov's scheme -- |
| -- |
The Tikhonov functional -- |
| -- |
Properties of a minimizing sequence -- |
| -- |
Other types of convergence -- |
| -- |
Equations with noisy data -- |
| -- |
Problems -- |
| -- |
Tikhonov's scheme for linear equations -- |
| -- |
The main convergence result -- |
| -- |
Elements of spectral theory -- |
| -- |
Minimizing sequences for linear equations |
| 505 00 - Formatted Contents Note |
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| Title |
A priori agreement between the regularization parameter and the error for equations with perturbed right-hand sides -- |
| -- |
The discrepancy principle -- |
| -- |
Approximation of a quasi-solution -- |
| -- |
Problems -- |
| -- |
The gradient scheme for linear equations -- |
| -- |
The technique of spectral analysis -- |
| -- |
A priori stopping rule -- |
| -- |
A posteriori stopping rule -- |
| -- |
Problems -- |
| -- |
Convergence rates for the approximation methods in the case of linear irregular equations -- |
| -- |
The source-type condition (STC) -- |
| -- |
STC for the gradient method -- |
| -- |
The saturation phenomena -- |
| -- |
Approximations in case of a perturbed STC -- |
| -- |
Accuracy of the estimates -- |
| -- |
Problems -- |
| -- |
Equations with a convex discrepancy functional by Tikhonov's method -- |
| -- |
Some difficulties associated with Tikhonov's method in case of a convex discrepancy functional |
| 505 00 - Formatted Contents Note |
|---|
| Title |
An illustrative example -- |
| -- |
Problems -- |
| -- |
Iterative regularization principle -- |
| -- |
The idea of iterative regularization -- |
| -- |
The iteratively regularized gradient method -- |
| -- |
Problems -- |
| -- |
The iteratively regularized Gauss -- Newton method -- |
| -- |
Convergence analysis -- |
| -- |
Further properties of IRGN iterations -- |
| -- |
A unified approach to the construction of iterative methods for irregular equations -- |
| -- |
The reverse connection control -- |
| -- |
Problems -- |
| -- |
The stable gradient method for irregular nonlinear equations -- |
| -- |
Solving an auxiliary finite dimensional problem by the gradient descent method -- |
| -- |
Investigation of a difference inequality -- |
| -- |
The case of noisy data -- |
| -- |
Problems -- |
| -- |
Relative computational efficiency of iteratively regularized methods -- |
| -- |
Generalized Gauss -- Newton methods -- |
| -- |
A more restrictive source condition |
| 505 00 - Formatted Contents Note |
|---|
| Title |
Comparison to iteratively regularized gradient scheme -- |
| -- |
Problems -- |
| -- |
Numerical investigation of two-dimensional inverse gravimetry problem -- |
| -- |
Problem formulation -- |
| -- |
The algorithm -- |
| -- |
Simulations -- |
| -- |
Problems -- |
| -- |
Iteratively regularized methods for inverse problem in optical tomography -- |
| -- |
Statement of the problem -- |
| -- |
Simple example -- |
| -- |
Forward simulation -- |
| -- |
The inverse problem -- |
| -- |
Numerical results -- |
| -- |
Problems -- |
| -- |
Feigenbaum's universality equation -- |
| -- |
The universal constants -- |
| -- |
Ill-posedness -- |
| -- |
Numerical algorithm for 2 ≤ z ≤ 12 -- |
| -- |
Regularized method for z ≥ 13 -- |
| -- |
Problems -- |
| -- |
Conclusion. |
| 505 00 - Formatted Contents Note |
|---|
| Title |
HKBU library |
| 518 ## - DATE/TIME AND PLACE OF AN EVENT NOTE |
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| DATE/TIME AND PLACE OF AN EVENT NOTE |
YT2025 M10 |
| 650 #0 - SUBJECT |
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| Topical term |
Differential equations, Partial |
| General subdivision |
Improperly posed problems. |
| 650 #0 - SUBJECT |
|---|
| Topical term |
Iterative methods (Mathematics) |
| 700 1# - PERSONAL NAME |
|---|
| Personal name |
Kokurin, M. I︠U︡. |
| 700 1# - PERSONAL NAME |
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| Personal name |
Smirnova, A. B. |
| 900 ## - Accession Number |
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| Accession Number |
= C.1 SDU |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Koha item type |
English Books |
| Source of classification or shelving scheme |
Library of Congress Classification |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| -- |
193027 |
| 650 #0 - SUBJECT |
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| -- |
193028 |
| 650 #0 - SUBJECT |
|---|
| -- |
193029 |
| 700 1# - PERSONAL NAME |
|---|
| -- |
193030 |
| 700 1# - PERSONAL NAME |
|---|
| -- |
193031 |
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