Variational methods for solving ill-posed extremal problems

Тихонов, А. Н.; Леонов, А. С.; Yagola, A. G.

doi:10.1007/978-94-017-5167-4_2

Cited by 119 publications

(192 citation statements)

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“…The system of equations (3) approximates an integral equation of the first kind and is therefore severely ill-conditioned (see, e.g., ref 31). Therefore, a regularization method should be used for the recovery of a decay time distribution from luminescence decay kinetics.…”

Section: Methodsmentioning

confidence: 99%

Luminescence Properties of Thiol-Stabilized CdTe Nanocrystals

et al. 1999

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Thiol-capped CdTe nanocrystals with cubic zinc blende structure are synthesized in aqueous solution. Their steady-state and time-resolved luminescence characteristics are studied at room and liquid nitrogen temperatures. A strong exciton luminescence peak at 2.3 eV dominates the emission spectrum of CdTe nanocrystals at room temperature, whereas the trap band centered at 2.0 eV undergoes substantial temperature quenching. Luminescence excitation spectra reveal different channels leading to radiative recombination via either excitons or traps. The mean luminescence decay time of CdTe nanocrystals at room temperature decreases from 120 ns at 1.94 eV to 20 ns at 2.43 eV. Luminescence decay kinetics of CdTe nanocrystals are strongly nonexponential and are described by extremely broad lifetime distributions lying within the range from a few hundred picoseconds to a few hundred nanoseconds.

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Section: Methodsmentioning

confidence: 99%

Luminescence Properties of Thiol-Stabilized CdTe Nanocrystals

et al. 1999

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“…However, in the case of perturbed boundary data, such an approach would produce a highly unstable solution and hence systems (16) and (24) should be solved, in a stable manner, by using e.g. the Tikhonov regularization method [7].…”

Section: Methods Of Fundamental Solutionsmentioning

confidence: 99%

MFS-based solution to two-dimensional linear thermoelasticity problems

Marin

Karageorghis

2012

WIT Transactions on Modelling and Simulation

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We propose the numerical approximation of the boundary and internal thermoelastic fields in the case of two-dimensional isotropic linear thermoelastic solids by combining the method of fundamental solutions (MFS) with the method of particular solutions (MPS). A particular solution of the non-homogeneous equations of equilibrium associated with a two-dimensional isotropic linear thermoelastic material is derived based on the MFS approximation of the boundary value problem for the heat conduction equation.

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“…See e.g. Engl et al [35] or the historical Tikhonov & Arsenin [75]. Throughout this paper we use the least squares norm, unless otherwise specified.…”

Section: Distributed Parameter Estimation and The Exponential Filter mentioning

confidence: 99%

Artificial time integration

2007

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Abstract.Many recent algorithmic approaches involve the construction of a differential equation model for computational purposes, typically by introducing an artificial time variable. The actual computational model involves a discretization of the now time-dependent differential system, usually employing forward Euler. The resulting dynamics of such an algorithm is then a discrete dynamics, and it is expected to be "close enough" to the dynamics of the continuous system (which is typically easier to analyze) provided that small -hence many -time steps, or iterations, are taken. Indeed, recent papers in inverse problems and image processing routinely report results requiring thousands of iterations to converge. This makes one wonder if and how the computational modeling process can be improved to better reflect the actual properties sought.In this article we elaborate on several problem instances that illustrate the above observations. Algorithms may often lend themselves to a dual interpretation, in terms of a simply discretized differential equation with artificial time and in terms of a simple optimization algorithm; such a dual interpretation can be advantageous. We show how a broader computational modeling approach may possibly lead to algorithms with improved efficiency.

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Variational methods for solving ill-posed extremal problems

Cited by 119 publications

References 0 publications

Luminescence Properties of Thiol-Stabilized CdTe Nanocrystals

Luminescence Properties of Thiol-Stabilized CdTe Nanocrystals

MFS-based solution to two-dimensional linear thermoelasticity problems

Artificial time integration

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