Adaptive choice of the Tikhonov regularization parameter to solve ill-posed linear algebraic equations via Liapunov Optimizing Control
暂无分享,去创建一个
[1] Mark A. Lukas,et al. Comparing parameter choice methods for regularization of ill-posed problems , 2011, Math. Comput. Simul..
[2] Chein-Shan Liu,et al. Optimally scaled vector regularization method to solve ill-posed linear problems , 2012, Appl. Math. Comput..
[3] Gene H. Golub,et al. Generalized cross-validation as a method for choosing a good ridge parameter , 1979, Milestones in Matrix Computation.
[4] Per Christian Hansen,et al. REGULARIZATION TOOLS: A Matlab package for analysis and solution of discrete ill-posed problems , 1994, Numerical Algorithms.
[5] Paul Tseng. Control perspectives on numerical algorithms and matrix problems , 2008, Math. Comput..
[6] A. N. Tikhonov,et al. Solutions of ill-posed problems , 1977 .
[7] ProblemsPer Christian HansenDepartment. The L-curve and its use in the numerical treatment of inverse problems , 2000 .
[8] Eugenius Kaszkurewicz,et al. Iterative methods as dynamical systems with feedback control , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).
[9] U. Ascher,et al. On fast integration to steady state and earlier times , 2008 .
[10] Jin Cheng,et al. Regularization Methods for Ill-Posed Problems , 2015, Handbook of Mathematical Methods in Imaging.
[11] Dianne P. O'Leary,et al. Deblurring Images: Matrices, Spectra, and Filtering (Fundamentals of Algorithms 3) (Fundamentals of Algorithms) , 2006 .
[12] Anil K. Jain. Fundamentals of Digital Image Processing , 2018, Control of Color Imaging Systems.
[13] S. Atluri,et al. Novel Algorithms Based on the Conjugate Gradient Method for Inverting Ill-Conditioned Matrices, and a New Regularization Method to Solve Ill-Posed Linear Systems , 2010 .
[14] U. Ascher,et al. Esaim: Mathematical Modelling and Numerical Analysis Gradient Descent and Fast Artificial Time Integration , 2022 .
[15] Chein-Shan Liu. A Dynamical Tikhonov Regularization for Solving Ill-posed Linear Algebraic Systems , 2013 .
[16] Dianne P. O'Leary,et al. The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems , 1993, SIAM J. Sci. Comput..
[17] H. Gfrerer. An a posteriori parameter choice for ordinary and iterated Tikhonov regularization of ill-posed problems leading to optimal convergence rates , 1987 .
[18] Eugenius Kaszkurewicz,et al. Control Perspectives on Numerical Algorithms And Matrix Problems (Advances in Design and Control) (Advances in Design and Control 10) , 2006 .
[19] Marek Rudnicki,et al. Regularization Parameter Selection in Discrete Ill-Posed Problems — The Use of the U-Curve , 2007, Int. J. Appl. Math. Comput. Sci..
[20] Misha Elena Kilmer,et al. Choosing Regularization Parameters in Iterative Methods for Ill-Posed Problems , 2000, SIAM J. Matrix Anal. Appl..
[21] Pierre-Alexandre Bliman,et al. Control-theoretic design of iterative methods for symmetric linear systems of equations , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.
[22] J. Borwein,et al. Two-Point Step Size Gradient Methods , 1988 .
[23] M. Hestenes,et al. Methods of conjugate gradients for solving linear systems , 1952 .
[24] Mostafa Kaveh,et al. Regularization and image restoration using differential equations , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.
[25] S. Atluri,et al. An Iterative Method Using an Optimal Descent Vector, for Solving an Ill-Conditioned System B x = b , Better and Faster than the Conjugate Gradient Method , 2011 .
[26] Dianne P. O'Leary,et al. Deblurring Images: Matrices, Spectra and Filtering , 2006, J. Electronic Imaging.