scholarly journals Converse Results, Saturation and Quasi-optimality for Lavrentiev Regularization of Accretive Problems

2017 ◽  
Vol 55 (3) ◽  
pp. 1315-1329 ◽  
Author(s):  
Robert Plato
Keyword(s):  
Lavrentiev Regularization ◽  
Converse Results

scholarly journals Converse Results for the Downlink Multicell Processing With Finite Backhaul Capacity

2019 ◽  
Vol 65 (1) ◽  
pp. 368-379
Author(s):  
Tianyu Yang ◽  
Nan Liu ◽  
Wei Kang ◽  
Shlomo Shamai Shitz
Keyword(s):  
Converse Results

scholarly journals ITERATED LAVRENTIEV REGULARIZATION FOR NONLINEAR ILL-POSED PROBLEMS

2009 ◽  
Vol 51 (2) ◽  
pp. 191-217 ◽  
Author(s):  
P. MAHALE ◽  
M. T. NAIR
Keyword(s):  
Nonlinear Operator ◽  
Optimal Error Estimate ◽  
Positive Real ◽  
Iterative Regularization ◽  
Optimal Error ◽  
Lavrentiev Regularization ◽  
Inexact Data ◽  
Ill Posed ◽  
Funct Anal ◽  
General Source

AbstractWe consider an iterated form of Lavrentiev regularization, using a null sequence (αk) of positive real numbers to obtain a stable approximate solution for ill-posed nonlinear equations of the form F(x)=y, where F:D(F)⊆X→X is a nonlinear operator and X is a Hilbert space. Recently, Bakushinsky and Smirnova [“Iterative regularization and generalized discrepancy principle for monotone operator equations”, Numer. Funct. Anal. Optim.28 (2007) 13–25] considered an a posteriori strategy to find a stopping index kδ corresponding to inexact data yδ with $\|y-y^\d \|\leq \d $ resulting in the convergence of the method as δ→0. However, they provided no error estimates. We consider an alternate strategy to find a stopping index which not only leads to the convergence of the method, but also provides an order optimal error estimate under a general source condition. Moreover, the condition that we impose on (αk) is weaker than that considered by Bakushinsky and Smirnova.

scholarly journals Optimal rates for Lavrentiev regularization with adjoint source conditions

2017 ◽  
Vol 87 (310) ◽  
pp. 785-801 ◽  
Author(s):  
Robert Plato ◽  
Peter Mathé ◽  
Bernd Hofmann
Keyword(s):  
Lavrentiev Regularization

scholarly journals On Converse Results for Secure Index Coding

2021 ◽  
Author(s):  
Yucheng Liu ◽  
Lawrence Ong ◽  
Parastoo Sadeghi ◽  
Neda Aboutorab ◽  
Arman Sharififar
Keyword(s):  
Index Coding ◽  
Converse Results
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