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A discrepancy principle for Tikhonov regularization with approximately specified data

M. Thamban Nair, Eberhard Schock (1998)

Annales Polonici Mathematici

Many discrepancy principles are known for choosing the parameter α in the regularized operator equation ( T * T + α I ) x α δ = T * y δ , | y - y δ | δ , in order to approximate the minimal norm least-squares solution of the operator equation Tx = y. We consider a class of discrepancy principles for choosing the regularization parameter when T*T and T * y δ are approximated by Aₙ and z δ respectively with Aₙ not necessarily self-adjoint. This procedure generalizes the work of Engl and Neubauer (1985), and particular cases of the results are applicable...

A functional model for a family of operators induced by Laguerre operator

Hatamleh Ra'ed (2003)

Archivum Mathematicum

The paper generalizes the instruction, suggested by B. Sz.-Nagy and C. Foias, for operatorfunction induced by the Cauchy problem T t : t h ' ' ( t ) + ( 1 - t ) h ' ( t ) + A h ( t ) = 0 h ( 0 ) = h 0 ( t h ' ) ( 0 ) = h 1 A unitary dilatation for T t is constructed in the present paper. then a translational model for the family T t is presented using a model construction scheme, suggested by Zolotarev, V., [3]. Finally, we derive a discrete functional model of family T t and operator A applying the Laguerre transform f ( x ) 0 f ( x ) P n ( x ) e - x d x where P n ( x ) are Laguerre polynomials [6, 7]. We show that the Laguerre transform...

A note on singular and degenerate abstract equations

Angelo Favini (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si considera l’equazione astratta B A 1 u + A 0 u = h , dove A i ( i = 0...

Adaptive wavelet methods for saddle point problems

Stephan Dahlke, Reinhard Hochmuth, Karsten Urban (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Recently, adaptive wavelet strategies for symmetric, positive definite operators have been introduced that were proven to converge. This paper is devoted to the generalization to saddle point problems which are also symmetric, but indefinite. Firstly, we investigate a posteriori error estimates and generalize the known adaptive wavelet strategy to saddle point problems. The convergence of this strategy for elliptic operators essentially relies on the positive definite character of the operator....

Asymptotic behaviour of stochastic semigroups.

Esther Dopazo (1990)

Extracta Mathematicae

The problem to be treated in this note is concerned with the asymptotic behaviour of stochastic semigroups, as the time becomes very large. The subject is largely motived by the Theory of Markov processes. Stochastic semigroups usually arise from pure probabilistic problems such as random walks stochastic differential equations and many others.An outline of the paper is as follows. Section one deals with the basic definitions relative to K-positivity and stochastic semigroups. Asymptotic behaviour...

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