A contribution to the conditioning theory of the indefinite least squares problems

Applied Numerical Mathematics - Tập 177 - Trang 137-159 - 2022
Shaoxin Wang1, Lingsheng Meng2
1School of Statistics and Data Science, Qufu Normal University, Qufu 273165, PR China
2College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, PR China

Tài liệu tham khảo

Arioli, 2007, A partial condition number for linear least squares problems, SIAM J. Matrix Anal. Appl., 29, 413, 10.1137/050643088 Baboulin, 2011, A contribution to the conditioning of the total least-squares problem, SIAM J. Matrix Anal. Appl., 32, 685, 10.1137/090777608 Ben-Israel, 2003 Björck, 2015 Bojanczyk, 2003, Solving the indefinite least squares problem by hyperbolic QR factorization, SIAM J. Matrix Anal. Appl., 24, 914, 10.1137/S0895479802401497 Bojanczyk, 2003, The equality constrained indefinite least squares problem: theory and algorithms, BIT, 43, 505, 10.1023/B:BITN.0000007020.58972.07 Bojanczyk, 2021, Algorithms for indefinite linear least squares problems, Linear Algebra Appl., 623, 104, 10.1016/j.laa.2020.09.006 Cao, 2003, A subspace error estimate for linear systems, SIAM J. Matrix Anal. Appl., 24, 787, 10.1137/S0895479801390649 Chandrasekaran, 1998, A stable and efficient algorithm for the indefinite linear least-squares problem, SIAM J. Matrix Anal. Appl., 20, 354, 10.1137/S0895479896302229 Cucker, 2007, On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems, Math. Comput., 76, 947, 10.1090/S0025-5718-06-01913-2 Diao, 2017, On condition numbers for least squares with quadric inequality constraint, Comput. Math. Appl., 73, 616, 10.1016/j.camwa.2016.12.033 Diao, 2018, Condition numbers for a linear function of the solution of the linear least squares problem with equality constraints, J. Comput. Appl. Math., 344, 640, 10.1016/j.cam.2018.05.050 Diao, 2018, Mixed and componentwise condition numbers for a linear function of the solution of the total least squares problem, Linear Algebra Appl., 544, 1, 10.1016/j.laa.2018.01.008 Diao, 2016, Structured condition numbers of structured Tikhonov regularization problem and their estimations, J. Comput. Appl. Math., 308, 276, 10.1016/j.cam.2016.05.023 Diao, 2019, Backward error and condition number analysis for the indefinite linear least squares problem, Int. J. Comput. Math., 96, 1603, 10.1080/00207160.2018.1467007 Diao, 2019, Linearized estimate of the backward error for the equality constrained indefinite least squares problem, East Asian J. Appl. Math., 9, 270, 10.4208/eajam.130518.170918 Gohberg, 1993, Mixed, componentwise, and structured condition numbers, SIAM J. Matrix Anal. Appl., 14, 688, 10.1137/0614049 Gohberg, 2005 Golub, 2013 Hassibi, 1996, Linear estimation in Krein spaces–part I: theory, IEEE Trans. Autom. Control, 41, 18, 10.1109/9.481605 Higham, 2002 Higham, 2003, J-Orthogonal matrices: properties and generation, SIAM Rev., 45, 504, 10.1137/S0036144502414930 Li, 2017, Partial condition number for the equality constrained linear least squares problem, Calcolo, 54, 1121, 10.1007/s10092-017-0221-8 Li, 2018, On the partial condition numbers for the indefinite least squares problem, Appl. Numer. Math., 123, 200, 10.1016/j.apnum.2017.09.006 Li, 2014, On mixed and componentwise condition numbers for indefinite least squares problem, Linear Algebra Appl., 448, 104, 10.1016/j.laa.2014.01.030 Liu, 2011, Preconditioned conjugate gradient methods for the solution of indefinite least squares problems, Calcolo, 48, 261, 10.1007/s10092-011-0039-8 Liu, 2010, Algebraic properties and perturbation results for the indefinite least squares problem with equality constraints, Int. J. Comput. Math., 87, 425, 10.1080/00207160802123433 Mastronardi, 2014, An algorithm for solving the indefinite least squares problem with equality constraints, BIT, 54, 201, 10.1007/s10543-013-0452-2 Mastronardi, 2015, A structurally backward stable algorithm for solving the indefinite least squares problem with equality constraints, IMA J. Numer. Anal., 35, 107, 10.1093/imanum/dru004 Rice, 1966, A theory of condition, SIAM J. Numer. Anal., 3, 287, 10.1137/0703023 Wang, 2018, On the condition number theory of the equality constrained indefinite least squares problem, Electron. J. Linear Algebra, 34, 619, 10.13001/1081-3810.3819 Wang, 2021, Conditioning theory of the equality constrained quadratic programming and its applications, Linear Multilinear Algebra, 69, 1161, 10.1080/03081087.2019.1623858 Xie, 2013, On condition numbers for the canonical generalized polar decomposition of real matrices, Electron. J. Linear Algebra, 26, 842, 10.13001/1081-3810.1691 Xu, 2004, A backward stable hyperbolic QR factorization method for solving indefinite least squares problem, J. Shanghai Univ., 8, 391, 10.1007/s11741-004-0049-8