Methods for solving incorrectly posed problems

V.A. Morozov ; translation editor, Z. Nashed ; translated by A.B. Aries

[目次]

  • 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.

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この本の情報

書名 Methods for solving incorrectly posed problems
著作者等 Morozov, Vladimir Alekseevich
Nashed, Z.
Aries A.B.
Morozov V.A.
書名別名 Reguli︠a︡rnye metody reshenii︠a︡ nekorrektno postavlennykh zadach
出版元 Springer-Verlag
刊行年月 c1984
版表示 Softcover reprint of the original 1st ed. 1984
ページ数 xviii, 257 p.
大きさ 24 cm
ISBN 3540960597
0387960597
NCID BA01051317
※クリックでCiNii Booksを表示
言語 英語
原文言語 ロシア語
出版国 アメリカ合衆国
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