A mollification regularization method for stable analytic continuation

Deng, Zhong Liang; Fu, Chu-Li; Feng, Xiaoli; Zhang, Yuanxiang

doi:10.1016/j.matcom.2010.11.011

Cited by 10 publications

(7 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [8], the authors used the modified Tikhonov regularization method to solve this problem. Recently, this problem has been studied by many researchers with different regularization methods [10][11][12][13]. In [14,15], the authors give an optimal filtering method and a wavelet method for stable analytic continuation, respectively.…”

Section: Problemmentioning

confidence: 99%

“…We give numerical results under the a posteriori choice rule. The a posteriori parameter µ is selected by (11). In these experiments, we fix the fractional parameter γ = 2/3 and noise level δ = 0.01.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Figure 2 shows the numerical results of the a posteriori parameter selection of Example 2. µ is selected by the discrepancy principle (11), where τ = 1.1, δ = 0.01. Figure 2a-f Table 2 shows the different error results for different y in Example 2.…”

Section: Example 2 the Function H Is Given Bymentioning

confidence: 99%

See 2 more Smart Citations

A Posteriori Fractional Tikhonov Regularization Method for the Problem of Analytic Continuation

Xue

Xiong

2021

Mathematics

View full text Add to dashboard Cite

In this paper, the numerical analytic continuation problem is addressed and a fractional Tikhonov regularization method is proposed. The fractional Tikhonov regularization not only overcomes the difficulty of analyzing the ill-posedness of the continuation problem but also obtains a more accurate numerical result for the discontinuity of solution. This article mainly discusses the a posteriori parameter selection rules of the fractional Tikhonov regularization method, and an error estimate is given. Furthermore, numerical results show that the proposed method works effectively.

show abstract

Section: Problemmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

See 1 more Smart Citation

A Posteriori Fractional Tikhonov Regularization Method for the Problem of Analytic Continuation

Xue

Xiong

2021

Mathematics

View full text Add to dashboard Cite

show abstract

“…Among the wide variety of smooth approximation methods, the method that stands out is the mollification method. This method was chosen because of the large number of benefits that it provides during the regularization of many ill-posed problems 25 – 29 , including efficiency, accuracy, robustness, and reduced costs. A detailed explanation of how we carry-out the mollification of (3) is found in the Methods section.…”

Section: Modelmentioning

confidence: 99%

Metastability for discontinuous dynamical systems under Lévy noise: Case study on Amazonian Vegetation

Serdukova

Zheng

Duan

et al. 2017

Sci Rep

View full text Add to dashboard Cite

For the tipping elements in the Earth’s climate system, the most important issue to address is how stable is the desirable state against random perturbations. Extreme biotic and climatic events pose severe hazards to tropical rainforests. Their local effects are extremely stochastic and difficult to measure. Moreover, the direction and intensity of the response of forest trees to such perturbations are unknown, especially given the lack of efficient dynamical vegetation models to evaluate forest tree cover changes over time. In this study, we consider randomness in the mathematical modelling of forest trees by incorporating uncertainty through a stochastic differential equation. According to field-based evidence, the interactions between fires and droughts are a more direct mechanism that may describe sudden forest degradation in the south-eastern Amazon. In modeling the Amazonian vegetation system, we include symmetric α-stable Lévy perturbations. We report results of stability analysis of the metastable fertile forest state. We conclude that even a very slight threat to the forest state stability represents L´evy noise with large jumps of low intensity, that can be interpreted as a fire occurring in a non-drought year. During years of severe drought, high-intensity fires significantly accelerate the transition between a forest and savanna state.

show abstract

“…Problems of this type have been considered, e. g., in [13,17,18,80]. They arise in different important applications such as in medical imaging, see [15].…”

Section: Proof (Sketch)mentioning

confidence: 99%

Conditional Stability Estimates for Ill-Posed PDE Problems by Using Interpolation

Tautenhahn

Hämarik

Hofmann

et al. 2013

Numerical Functional Analysis and Optimization

View full text Add to dashboard Cite

Abstract. The focus of this paper is on conditional stability estimates for illposed inverse problems in partial differential equations. Conditional stability estimates have been obtained in the literature by a couple different methods. In this paper we propose a method called interpolation method, which is based on interpolation in variable Hilbert scales. We are going to work out the theoretical background of this method and show that optimal conditional stability estimates are obtained. The capability of our method is illustrated by a comprehensive collection of different inverse and ill-posed PDE problems containing elliptic and parabolic problems, one source problem and the problem of analytic continuation.

show abstract

A mollification regularization method for stable analytic continuation

Cited by 10 publications

References 21 publications

A Posteriori Fractional Tikhonov Regularization Method for the Problem of Analytic Continuation

A Posteriori Fractional Tikhonov Regularization Method for the Problem of Analytic Continuation

Metastability for discontinuous dynamical systems under Lévy noise: Case study on Amazonian Vegetation

Conditional Stability Estimates for Ill-Posed PDE Problems by Using Interpolation

Contact Info

Product

Resources

About