Error bounds for Trotter-type formulas for self-adjoint operators

1993 ◽  
Vol 27 (3) ◽  
pp. 217-219 ◽  
Author(s):  
Dzh L. Rogava
Keyword(s):  
Error Bounds ◽  
Adjoint Operators

Convergence Rates For Lavrentiev-Type Regularization In Hilbert Scales

2008 ◽  
Vol 8 (3) ◽  
pp. 279-293 ◽  
Author(s):  
M.T. NAIR ◽  
U. TAUTENHAHN
Keyword(s):  
Error Bounds ◽  
Convergence Rates ◽  
Noisy Data ◽  
Regularization Methods ◽  
Operator Equations ◽  
Optimal Error ◽  
Regularization Scheme ◽  
Data Regularization ◽  
Ill Posed ◽  
Adjoint Operators

AbstractFor solving linear ill-posed problems with noisy data regularization methods are required. We analyze a simplified regularization scheme in Hilbert scales for operator equations with nonnegative self-adjoint operators. By exploiting the op-erator monotonicity of certain functions, order-optimal error bounds are derived that characterize the accuracy of the regularized approximations. These error bounds have been obtained under general smoothness conditions.

scholarly journals New Čebyšev Type Inequalities and Applications for Functions of Self-Adjoint Operators on Complex Hilbert Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Mohammad W. Alomari
Keyword(s):  
Hilbert Spaces ◽  
Error Bounds ◽  
Čebyšev Functional ◽  
Adjoint Operators

Several new error bounds for the Čebyšev functional under various assumptions are proved. Applications for functions of self-adjoint operators on complex Hilbert spaces are provided as well.

scholarly journals Metric Fourier Approximation of Set-Valued Functions of Bounded Variation

2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Elena E. Berdysheva ◽  
Nira Dyn ◽  
Elza Farkhi ◽  
Alona Mokhov
Keyword(s):  
Fourier Series ◽  
Bounded Variation ◽  
Error Bounds ◽  
Metric Spaces ◽  
Hausdorff Metric ◽  
Dirichlet Kernel ◽  
Partial Sums ◽  
Functions Of Bounded Variation ◽  
Moduli Of Continuity ◽  
Fourier Approximation

AbstractWe introduce and investigate an adaptation of Fourier series to set-valued functions (multifunctions, SVFs) of bounded variation. In our approach we define an analogue of the partial sums of the Fourier series with the help of the Dirichlet kernel using the newly defined weighted metric integral. We derive error bounds for these approximants. As a consequence, we prove that the sequence of the partial sums converges pointwisely in the Hausdorff metric to the values of the approximated set-valued function at its points of continuity, or to a certain set described in terms of the metric selections of the approximated multifunction at a point of discontinuity. Our error bounds are obtained with the help of the new notions of one-sided local moduli and quasi-moduli of continuity which we discuss more generally for functions with values in metric spaces.

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