Many discrepancy principles are known for choosing the parameter α in the regularized operator equation $(T*T+\alpha I)x_{\alpha }^{\delta }=T*y^{\delta }$, $|y-y^{\delta }|\le \delta$, 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 $T*y^{\delta }$ are approximated by Aₙ and $z{ₙ}^{\delta }$ 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...

In this paper we obtain a general fixed point theorem for an affine mapping in Banach space. As an application of this theorem we study existence of periodic solutions to the equations of the linear elasticity theory.

The paper generalizes the instruction, suggested by B. Sz.-Nagy and C. Foias, for operatorfunction induced by the Cauchy problem $$T_t:\left\{\begin{array}{c}t{h}^{\text{'}\text{'}}\left(t\right)+(1-t)h^{\text{'}}\left(t\right)+Ah\left(t\right)=0\hfill \\ h\left(0\right)=h_0\left(t{h}^{\text{'}}\right)\left(0\right)=h_1\hfill \end{array}\right.$$ 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 $$f\left(x\right)\to {\int }_0^{\infty }f\left(x\right)P_n\left(x\right)e^{-x}dx$$ where $P_n\left(x\right)$ are Laguerre polynomials [6, 7]. We show that the Laguerre transform...

Si considera l’equazione astratta $B{A}_{1}u+A_{0}u=h$, dove $A_i$$ ( i = 0... A posteriori estimations of approximate solutions for some types of boundary value problems Kodnár, Rudolf (1986) Equadiff 6 A Problem of Mixed Interpolation. Robin E. Harte (1975) Mathematische Zeitschrift A product integral representation of the generalized inverse Charles W. Groetsch (1975) Commentationes Mathematicae Universitatis Carolinae Absorbers: Definitions, properties and applications. Belitskii, G. (1998) Discrete Dynamics in Nature and Society Accelerated Landweber iterations for the solution of ill-posed equations. Martin Hanke (1991/1992) Numerische Mathematik Adaptive wavelet methods for saddle point problems Stephan Dahlke, Reinhard Hochmuth, Karsten Urban (2000) ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 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.... Algebraic theory of right invertible operators D. Przeworska-Rolewicz (1973) Studia Mathematica An equational approach to products of relatively regular operators. S.R. Caradus (1977) Aequationes mathematicae Approximate solutions of equations defined by complex spherical multiplier operators. Oliveira, C.P. (2005) Journal of Applied Mathematics Approximating the fixed points of some nonlinear operator equations Ioannis K. Argyros (1988) Mathematica Slovaca 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... Asymptotic optimality of generalized cross-validation for choosing the regularization parameter. Mark A. Lukas (1993/1994) Numerische Mathematik Currently displaying 1 – 20 of 20 Page 1 $