|
|
|
|
LEADER |
00000nam a22000005i 4500 |
001 |
b3202723 |
003 |
MWH |
005 |
20190619120128.0 |
007 |
cr nn 008mamaa |
008 |
121227s1984 xxu| s |||| 0|eng d |
020 |
|
|
|a 9781461252801
|
024 |
7 |
|
|a 10.1007/978-1-4612-5280-1
|2 doi
|
035 |
|
|
|a (DE-He213)978-1-4612-5280-1
|
050 |
|
4 |
|a E-Book
|
072 |
|
7 |
|a PBKS
|2 bicssc
|
072 |
|
7 |
|a MAT021000
|2 bisacsh
|
072 |
|
7 |
|a PBKS
|2 thema
|
100 |
1 |
|
|a Morozov, V.A.
|e author.
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
|
245 |
1 |
0 |
|a Methods for Solving Incorrectly Posed Problems
|h [electronic resource] /
|c by V.A. Morozov ; edited by Z. Nashed.
|
250 |
|
|
|a 1st ed. 1984.
|
264 |
|
1 |
|a New York, NY :
|b Springer New York :
|b Imprint: Springer,
|c 1984.
|
300 |
|
|
|a 257 p.
|b online resource.
|
336 |
|
|
|a text
|b txt
|2 rdacontent
|
337 |
|
|
|a computer
|b c
|2 rdamedia
|
338 |
|
|
|a online resource
|b cr
|2 rdacarrier
|
347 |
|
|
|a text file
|b PDF
|2 rda
|
490 |
1 |
|
|a Springer eBook Collection
|
505 |
0 |
|
|a 1. The Regularization Method -- Section 1. The Basic Problem for Linear Operators -- Section 2. The Approximation of the Solution of the Basic Problem -- Section 3. The Euler Variation Inequality. Estimation of Accuracy -- Section 4. Stability of Regularized Solutions -- Section 5. Approximation of the Admissible Set. Choice of the Basis -- 2. Criteria for Selection of Regularization Parameter -- Section 6. Some Properties of Regularized Solutions -- Section 7. Methods for Choosing the Parameter: Case of Exact Information -- Section 8. The Residual Method and the Method of Quasi-solutions: Case of Exact Information -- Section 9. Properties of the Auxiliary Functions -- Section 10. Criteria for the Choice of a Parameter: Case of Inexact Data -- 3. Regular Methods for Solving Linear and Nonlinear Ill-Posed Problems -- Section 11. Regularity of Approximation Methods -- Section 12. The Theory of Accuracy of Regular Methods -- Section 13. The Computation of the Estimation Function -- Section 14. Examples of Regular Methods -- Section 15. The Principle of Residual Optimality for Approximate Solutions of Equations with Nonlinear Operators -- Section 16. The Regularization Method for Nonlinear Equations -- 4. The Problem of Computation and the General Theory of Splines -- Section 17. The Problem of Computation and the Parameter Identification Problem -- Section 18. Properties of Smoothing Families of Operators -- Section 19. The Optimality of Smoothing Algorithms -- Section 20. The Differentiation Problem and Algorithms of Approximation of the Experimental Data -- Section 21.The Theory of Splines and the Problem of Stable Computation of Values of an Unbounded Operator -- Section 22. Approximate Solution of Operator Equations Using Splines -- Section 23. Recovering the Solution of the Basic Problem From Approximate Values of the Functiona1s -- 5. Regular Methods for Special Cases of the Basic Problem. Algorithms for Choosing the Regularization Parameter -- Section 24. Pseudosolutions -- Section 25. Optimal Regularization -- Section 26. Numerical Algorithms for Regularization Parameters -- Section 27. Heuristic Methods for Choosing a Parameter -- Section 28. The Investigation of Adequacy of Mathematical Models.
|
520 |
|
|
|a Some problems of mathematical physics and analysis can be formulated as the problem of solving the equation f € F, (1) Au = f, where A: DA C U + F is an operator with a non-empty domain of definition D , in a metric space U, with range in a metric space F. The metrics A on U and F will be denoted by P and P ' respectively. Relative u F to the twin spaces U and F, J. Hadamard P-06] gave the following defini tion of correctness: the problem (1) is said to be well-posed (correct, properly posed) if the following conditions are satisfied: (1) The range of the value Q of the operator A coincides with A F ("sol vabi li ty" condition); (2) The equality AU = AU for any u ,u € DA implies the I 2 l 2 equality u = u ("uniqueness" condition); l 2 (3) The inverse operator A-I is continuous on F ("stability" condition). Any reasonable mathematical formulation of a physical problem requires that conditions (1)-(3) be satisfied. That is why Hadamard postulated that any "ill-posed" (improperly posed) problem, that is to say, one which does not satisfy conditions (1)-(3), is non-physical. Hadamard also gave the now classical example of an ill-posed problem, namely, the Cauchy problem for the Laplace equation.
|
590 |
|
|
|a Loaded electronically.
|
590 |
|
|
|a Electronic access restricted to members of the Holy Cross Community.
|
650 |
|
0 |
|a Numerical analysis.
|
690 |
|
|
|a Electronic resources (E-books)
|
700 |
1 |
|
|a Nashed, Z.
|e editor.
|4 edt
|4 http://id.loc.gov/vocabulary/relators/edt
|
710 |
2 |
|
|a SpringerLink (Online service)
|
773 |
0 |
|
|t Springer eBooks
|
830 |
|
0 |
|a Springer eBook Collection.
|
856 |
4 |
0 |
|u https://holycross.idm.oclc.org/login?auth=cas&url=https://doi.org/10.1007/978-1-4612-5280-1
|3 Click to view e-book
|t 0
|
907 |
|
|
|a .b32027230
|b 04-18-22
|c 02-26-20
|
998 |
|
|
|a he
|b 02-26-20
|c m
|d @
|e -
|f eng
|g xxu
|h 0
|i 1
|
912 |
|
|
|a ZDB-2-SMA
|
912 |
|
|
|a ZDB-2-BAE
|
950 |
|
|
|a Mathematics and Statistics (Springer-11649)
|
902 |
|
|
|a springer purchased ebooks
|
903 |
|
|
|a SEB-COLL
|
945 |
|
|
|f - -
|g 1
|h 0
|j - -
|k - -
|l he
|o -
|p $0.00
|q -
|r -
|s b
|t 38
|u 0
|v 0
|w 0
|x 0
|y .i21158873
|z 02-26-20
|
999 |
f |
f |
|i 5ab2a58c-da05-501c-b2dd-0a6e9fe5684a
|s 45545147-da83-5b92-a273-7ae0484ff8fd
|t 0
|
952 |
f |
f |
|p Online
|a College of the Holy Cross
|b Main Campus
|c E-Resources
|d Online
|t 0
|e E-Book
|h Library of Congress classification
|i Elec File
|