References
- G. Arfken, Mathematical Methods for Physicists, Third edition, Academic Press, Orlando, FL, USA, 1985.
- D. Boley and G. H. Golub, Inverse eigenvalue problems for band matrices, Technical Report STAN-CS-77-623, Department of Computer Science, Stanford University, Stanford. CA., 1977.
- L. Elden, Algorithms for the regularization of ill-conditioned least squares problems, BIT 17 (1977), no. 2, 134-145. https://doi.org/10.1007/BF01932285
- G. H. Golub, P. C. Hansen, and D. P. O'Leary, Tikhonov regularization and total least squares, SIAM J. Matrix Anal. Appl. 21 (1999), no. 1, 185-194. https://doi.org/10.1137/S0895479897326432
- H. Guo and R. A. Renaut, A regularized total least squares algorithm, Total least squares and errors-in-variables modeling (Leuven, 2001), 57-66, Kluwer Acad. Publ., Dordrecht, 2002.
- P. C. Hansen, Regularization, GSVD and truncated GSVD, BIT 29 (1989), no. 3, 491-504. https://doi.org/10.1007/BF02219234
- P. C. Hansen, Analysis of discrete ill-posed problems by means of the L-curve, SIAM Rev. 34 (1992), no. 4, 561-580. https://doi.org/10.1137/1034115
- P. C. Hansen, Regularization Tools: A Matlab package for analysis and solution of discrete ill-posed problems, Numer. Algorithms 6 (1994), no. 1-2, 1-35. https://doi.org/10.1007/BF02149761
- P. C. Hansen, Rank-Decient and Discrete Ill-Posed Problems. Numerical Aspects of Linear Inversion, SIAM, Philadelphia, 1998.
- P. C. Hansen and D. P. O'Leary, The use of the L-curve in the regularization of discrete ill-posed problems, SIAM J. Sci. Comput. 14 (1993), no. 6, 1487-1503. https://doi.org/10.1137/0914086
- J. Lampe, Solving Regularized Total Least Squares Problems Based on Eigenproblems, Ph.D. Thesis, Hamburg University of Technology, Institute of Numerical Simulation, 2010.
- C. L. Lawson and R. J. Hanson, Solving Least Squares Problems, Solving Least Squares Problems, Classics in Applied Mathematics, Society for Industrial and Applied Mathematics, 1987.
- G. Lee, H. Fu, and J. L. Barlow, Fast high-resolution image reconstruction using Tikhonov regularization based total least squares, SIAM J. Sci. Comput. 35 (2013), no. 1, B275-B290. https://doi.org/10.1137/110850591
- K. Miller, Least squares methods for ill-posed problems with a prescribed bound, SIAM J. Math. Anal. 1 (1970), no. 1, 52-74. https://doi.org/10.1137/0501006
- J. Nocedal and S. J. Wright, Numerical Optimization, Springer-Verlag, Berlin, 2000.
- C. C. Paige and M. A. Saunders, LSQR: An algorithm for sparse linear equations and sparse least squares, ACM Trans. Math. Software 8 (1982), no. 1, 43-71. https://doi.org/10.1145/355984.355989
- T. Reginska, A regularization parameter in discrete ill-posed problems, SIAM J. Sci. Comput. 17 (1996), no. 3, 740-749. https://doi.org/10.1137/S1064827593252672
- R. Renaut and H. Guo, Efficient algorithms for solution of regularized total least squares, SIAM J. Matrix Anal. Appl. 26 (2004), no. 2, 457-476. https://doi.org/10.1137/S0895479802419889
- J. D. Riley, Solving systems of linear equations with a positive denite symmetric but possibly ill-conditioned matrix, Math. Tables Aids Comput. 9 (1955), 96-101. https://doi.org/10.2307/2002065
- A. N. Tikhonov and V. Y. Arsenin, Solution of Ill-Posed Problems, Winston, Washington D.C., 1977.