An Optimally Generalized Steepest-Descent Algorithm for Solving Ill-Posed Linear Systems
Journal of Applied Mathematics, 2013 It is known that the steepest-descent method converges normally at the first few iterations, and then it slows down. We modify the original steplength and descent direction by an optimization argument with the new steplength as being a merit function to ...
Chein-Shan Liu
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Logarithmic regularization of non-autonomous non-linear ill-posed problems in Hilbert spaces
Electronic Journal of Differential Equations, 2017 The regularization of non-autonomous non-linear ill-posed problems is established using a logarithmic approximation originally proposed by Boussetila and Rebbani, and later modified by Tuan and Trong.
Matthew Fury
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Doppler Positioning with LEO Mega-Constellation: Equation Properties and Improved Algorithm
Remote SensingDoppler positioning, as an early form of positioning, has regained significant research interest in the context of Low Earth Orbit (LEO) satellites.Given the LEO mega-constellation scenario, the objective function of Doppler positioning manifests ...
Zichen Xu +6 more
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The stability of images taken in computed tomography by back-projection method
Біофізичний вісник, 2017 Background: The back-projection method is quite widespread in the modern computed tomography and there are not principled critical comments addressed to it in the scientific literature. But there are reasons for such comments.
Л. А. Булавін +3 more
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A quasi-boundary value method for regularizing nonlinear ill-posed problems
Electronic Journal of Differential Equations, 2009 In this article, a modified quasi-boudary regularization method for solving nonlinear backward heat equation is given. Sharp error estimates for the approximate solutions, and numerical examples to illustrate the effectiveness our method are provided.
Dang Duc Trong +2 more
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The parameter Houlihan: A solution to high-throughput identifiability indeterminacy for brutally ill-posed problems. [PDF]
Math Biosci, 2019 Albers DJ +3 more
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Well-Posed and Ill-Posed Boundary Value Problems for PDE
Abstract and Applied Analysis, 2012 Allaberen Ashyralyev +4 more
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Classification of structural MRI images in Alzheimer's disease from the perspective of ill-posed problems. [PDF]
PLoS One, 2012 Casanova R +3 more
europepmc +1 more source
Well-Posed and Ill-Posed Boundary Value Problems for PDE 2013
Abstract and Applied Analysis, 2013 Allaberen Ashyralyev +5 more
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Final-value problem for a weakly-coupled system of structurally damped waves
Electronic Journal of Differential Equations, 2018 We consider the final-value problem of a system of strongly-damped wave equations. First of all, we find a solution of the system, then by an example we show the problem is ill-posed.
Nguyen Huy Tuan +3 more
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