On the quasi-optimal rules for the choice of the regularization parameter in case of a noisy operator

Autor:	Uno Hämarik, Toomas Raus
Rok vydání:	2011
Předmět:	Computational Mathematics Mathematical optimization Operator (computer programming) Monotone polygon Property (philosophy) Quality (physics) Applied Mathematics Inverse A priori and a posteriori Regularization (mathematics) Oracle inequality Mathematics
Zdroj:	Advances in Computational Mathematics. 36:221-233
ISSN:	1572-9044 1019-7168
Popis:	A usual way to characterize the quality of different a posteriori parameter choices is to prove their order-optimality on the different sets of solutions. In paper by Raus and Hamarik (J Inverse Ill-Posed Probl 15(4):419---439, 2007) we introduced the property of the quasi-optimality to characterize the quality of the rule of the a posteriori choice of the regularization parameter for concrete problem Au?=?f in case of exact operator and discussed the quasi-optimality of different well-known rules for the a posteriori parameter choice as the discrepancy principle, the modification of the discrepancy principle, balancing principle and monotone error rule. In this paper we generalize the concept of the quasi-optimality for the case of a noisy operator and concretize results for the mentioned parameter choice rules.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::72d81763add7ecd989ef9b7f368b4259 https://doi.org/10.1007/s10444-011-9203-6 Zobrazit plný text záznamu Full text from SpringerLink