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A Regularization Parameter in Discrete Ill-Posed Problems
SIAM Journal of Scientific Computing, 1996The author considers the Tikhonov regularization method for the discrete ill-posed problem of minimizing \[ J_\alpha(u)=|Ku-f|^2+\alpha|u|^2, \] where \(K\) is an \(m\times n\) matrix with a large condition number, \(m\geq n\), and \(\alpha>0\). The Euclidean norm is used.
exaly +3 more sources
Regularizing Newton--Kaczmarz Methods for Nonlinear Ill-Posed Problems
SIAM Journal on Numerical Analysis, 2006Martin Bürger, Barbara Kaltenbacher
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Conditional Stability Estimates for Ill-Posed PDE Problems by Using Interpolation
Numerical Functional Analysis and Optimization, 2013U Tautenhahn +2 more
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On Converse and Saturation Results for Tikhonov Regularization of Linear Ill-Posed Problems
SIAM Journal on Numerical Analysis, 1997exaly
On the discrete linear ill‐posed problems
Mathematical Modelling and Analysis, 1999 An inverse problem of photo‐acoustic spectroscopy of semiconductors is investigated. The main problem is formulated as the integral equation of the first kind.
A. A. Stepanov
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Ill-posed inverse problems in economics [PDF]
Annual Review of Economics, 2013 A parameter of an econometric model is identified if there is a one-to-one or many-to-one mapping from the population distribution of the available data to the parameter.
Joel L. Horowitz, Horowitz, Joel
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Noise Models for Ill-Posed Problems
, 2014 The standard view of noise in ill-posed problems is that it is either deterministic and small (strongly bounded noise) or random and large (not necessarily small).
Vincent LaRiccia +5 more
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Economic Cycles of Carnot Type
Entropy, 2021 Originally, the Carnot cycle was a theoretical thermodynamic cycle that provided an upper limit on the efficiency that any classical thermodynamic engine can achieve during the conversion of heat into work, or conversely, the efficiency of a ...
Constantin Udriste +2 more
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Discrete and Continuous Models and Applied Computational Science, 2023 The paper describes a grid method for solving an ill-posed problem for the Fredholm equation of the first kind using the A. N. Tikhonov regularizer. The convergence theorem for this method was formulated and proved.
Aleksandr A. Belov
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