基于光滑全变分的修正tikhonov正则化方法求解线性不适定问题

IF 0.6 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Eurasian Journal of Mathematical and Computer Applications Pub Date : 2021-06-01 DOI:10.32523/2306-6172-2021-9-2-88-100

V. Vasin, V. Belyaev

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引用次数: 0

摘要

研究了一类在Hadamard意义上不适定的线性算子方程。假设其解可表示为光滑和不连续分量的和。为了构造一个稳定的近似解，我们使用改进的Tikhonov方法，将稳定泛函作为光滑分量的Lebesgue范数和不连续分量的光滑bv范数的和。证明了正则解及其有限维近似的存在性、唯一性和收敛性定理。并给出了数值实验结果。

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THE MODIFIED TIKHONOV REGULARIZATION METHOD WITH THE SMOOTHED TOTAL VARIATION FOR SOLVING THE LINEAR ILL-POSED PROBLEMS

We investigate a linear operator equation of the first kind that is ill-posed in the Hadamard sence. It is assumed that its solution is representable as a sum of smooth and discontinuous components. To construct a stable approximate solutions, we use the modified Tikhonov method with the stabilizing functional as a sum of the Lebesgue norm for the smooth component and a smoothed BV-norm for the discontinuous component. Theorems of exis- tence, uniqueness, and convergence both the regularized solutions and its finite-dimentional approximations are proved. Also, results of numerical experiments are presented.

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来源期刊

Eurasian Journal of Mathematical and Computer Applications MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

1.40

自引率

0.00%

发文量

期刊介绍： Eurasian Journal of Mathematical and Computer Applications (EJMCA) publishes carefully selected original research papers in all areas of Applied mathematics first of all from Europe and Asia. However papers by mathematicians from other continents are also welcome. From time to time Eurasian Journal of Mathematical and Computer Applications (EJMCA) will also publish survey papers. Eurasian Mathematical Journal publishes 4 issues in a year. A working language of the journal is English. Main topics are: - Mathematical methods and modeling in mechanics, mining, biology, geophysics, electrodynamics, acoustics, industry. - Inverse problems of mathematical physics: theory and computational approaches. - Medical and industry tomography. - Computer applications: distributed information systems, decision-making systems, embedded systems, information security, graphics.