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Extension of Tikhonov regularization method using linear fractional programming
Journal of Computational and Applied Mathematics, 2020Given a real $m\times n$ matrix $A$ with $m\geq n$ and a noisy vector $b$, this paper focuses on the following least-squares problem: $\min_{x\in \mathbb{R}^n}\|Ax-b\|^2$. Here $\|\cdot\|$ is the Euclidean norm. This problem is commonly studied in the framework of the Tikhonov regularization which consists of solving the regularized least-squares ...
Somaieh Mohammady, M. R. Eslahchi
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On the condition number of matrices arising in the tikhonov regularization method
Acta Applicandae Mathematicae, 1994An integral equation of the first kind (1) \((Kf)(s) = \int^ b_ a k(s,t) f(t)dt = g(s)\), \(K : L^ 2 [a,b] \to L^ 2 [a,b]\), \(k \in L^ 2 ([a,b] \times [a,b])\) is known to be an ill-posed problem. As an expression of this ill-posedness, for many numerical methods (e.g., Galerkin, collocation) the approximate solution of (1) fails in general to the ...
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A Tikhonov-type regularization method for Caputo fractional derivative
Numerical AlgorithmszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nguyen Van Duc +5 more
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A Tikhonov Regularization Method for Solving an Inverse Heat Source Problem
Bulletin of the Malaysian Mathematical Sciences Society, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yang, Shuping, Xiong, Xiangtuan
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Convergence Rates of the Hilbert Uniqueness Method via Tikhonov Regularization
Journal of Optimization Theory and Applications, 1999A parabolic differential equation on \([0,1]\times [0,T]\) with Dirichlet data and homogeneous initial data of the following form is considered \[ {\partial y\over\partial t}-{\partial\over\partial x} \Biggl(a(x){\partial y\over\partial x}\Biggr)= 0, \] \[ y(0,x)= 0,\quad y(t,0)= \nu_0(t),\quad y(t,1)= \nu_1(t), \] with diffusion coefficient \(a(x)\in ...
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Image edge detection with the use of the Tikhonov regularization method
Moscow University Computational Mathematics and Cybernetics, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tsibanov, V. N., Krylov, A. S.
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On Morozov’s Method for Tikhonov Regularization as an Optimal Order Yielding Algorithm
Zeitschrift für Analysis und ihre Anwendungen, 1999It is shown that Tikhonov regularization for an ill-posed operator equation Kx = y using a possibly unbounded regularizing operator L yields an order-optimal ...
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An improved Tikhonov regularization method combined with the exponential filter function
Journal of Computational Methods in Sciences and EngineeringTikhonov regularization is one of the most popular methods for solving linear discrete ill-posed problems. This approach involves transforming the original problem into a penalized least-squares problem, yielding a solution that exhibits greater robustness against data inaccuracies and computational errors that may occur during the solving process. The
Xiaoniu Zeng +4 more
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Tikhonov regularization method for dynamic load identification
Fourth International Conference on Artificial Intelligence and Electromechanical Automation (AIEA 2023), 2023Pengfei Cai +3 more
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