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Research Article

Condition numbers of the mixed least squares-total least squares problem revisited

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Pages 2144-2162 | Received 17 Nov 2020, Accepted 05 May 2022, Published online: 01 Jul 2022

References

  • Björck Å. Numerical methods for least squares problems. Philadelphia: SIAM; 1996.
  • Golub GH, Van Loan CF. An analysis of the total least squares problem. SIAM J Numer Anal. 1980;17(6):883–893.
  • Liu QH, Chen CP, Zhang Q. Perturbation analysis for total least squares problems with linear equality constraint. Appl Numer Math. 2021;161:69–81.
  • Liu QH, Jin SF, Yao L, et al. The revisited total least squares problems with linear equality constraint. Appl Numer Math. 2020;152:275–284.
  • Liu QH, Wang MH. On the weighting method for mixed least squares-total least squares problems. Numer Linear Algebra Appl. 2017;24(5):e2094.
  • Paige CC, Wei MS. Analysis of the generalized total least squares problem AX≈B when some columns of A are free of error. Numer Math. 1993;65(1):177–202.
  • Yan SJ, Fan JY. The solution set of the mixed LS-TLS problem. Int J Comput Math. 2001;77(4):545–561.
  • Gleser LJ. Estimation in a multivariate "errors in variables" regression model: large sample results. Ann Statist. 1981;9:24–44.
  • Stoica P, Söderström T. Bias correction in least squares identification. Int J Control. 1982;35(3):449–457.
  • Van Huffel S, Vandewalle J. Comparison of total least squares and instrumental variable methods for parameter estimation of transfer function models. Int J Control. 1989;50:1039–1056.
  • Golub GH, Van Loan CF. Matrix computation. 4th ed. Baltimore: Johns Hopkins University Press; 2013.
  • Van Huffel S, Vandewalle J. The total least-squares problem: computational aspects and analysis. In: Frontier in applied mathematics. Philadelphia: SIAM; 1991.
  • Xie PP, Xiang H, Wei YM. Randomized algorithms for total least squares problems. Numer Linear Algebra Appl. 2018;26:e2219.
  • Zhou LM, Lin LJ, Wei YM, et al. Perturbation analysis and condition numbers of scaled total least squares problems. Numer Algorithms. 2009;51(3):381–399.
  • Baboulin M, Gratton S. A contribution to the conditioning of the total least squares problem. SIAM J Matrix Anal Appl. 2011;32(3):685–699.
  • Jia ZX, Li BY. On the condition number of the total least squares problem. Numer Math. 2013;125(1):61–87.
  • Li BY, Jia ZX. Some results on condition numbers of the scaled total least squares problem. Linear Algebra Appl. 2011;435(3):674–686.
  • Wang SX, Li HY, Yang H. A note on the condition number of the scaled total least squares problem. Calcolo. 2018;55:46.
  • Xie PP, Xiang H, Wei YM. A contribution to perturbation analysis for total least squares problems. Numer Algorithms. 2017;75(2):381–395.
  • Diao HA, Sun Y. Mixed and componentwise condition numbers for a linear function of the solution of the total least squares problem. Linear Algebra Appl. 2018;544:1–29.
  • Meng QL, Diao HA, Bai ZJ. Condition numbers for the truncated total least squares problem and their estimations. Numer Linear Algebra Appl. 2021;28(5):e2369.
  • Meng LS, Zheng B, Wei YM. Condition numbers of the multi-dimensional total least squares problems having more than one solution. Numer Algorithms. 2020;84:887–908.
  • Zheng B, Meng LS, Wei YM. Condition numbers of the multidimensional total least squares problem. SIAM J Matrix Anal Appl. 2017;38(3):924–948.
  • Van Huffel S, Vandewalle J. Analysis and properties of the generalized total least squares problem AX≈B when some or all columns in A are subject to error. SIAM J Matrix Anal Appl. 1989;10:294–315.
  • Zheng B, Yang ZS. Perturbation analysis for mixed least squares-total least squares problems. Numer Linear Algebra Appl. 2019;26:e2239.
  • Langville AN, Stewart WJ. The Kronecker product and stochastic automata networks. J Comput Appl Math. 2004;167:429–447.
  • Graham A. Kronecker products and matrix calculus with application. New York: Wiley; 1981.
  • Rice JR. A theory of condition. SIAM J Numer Anal. 1966;3:287–310.
  • Geurts AJ. A contribution to the theory of condition. Numer Math. 1982;39:85–96.
  • Gohberg I, Koltracht I. Mixed, componentwise, and structured condition numbers. SIAM J Matrix Anal Appl. 1993;14:688–704.
  • Cucker F, Diao HA, Wei YM. On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems. Math Comp. 2007;76(258):947–963.
  • Higham NJ. Accuracy and stability of numerical algorithms. 2nd ed. Philadelphia: SIAM; 2002.
  • Diao HA, Wei YM, Xie PP. Small sample statistical condition estimation for the total least squares problem. Numer Algorithms. 2017;75(2):1–21.
  • Björck Å, Heggernes P, Matstoms P. Methods for large scale total least squares problems. SIAM J Matrix Anal Appl. 2000;22(2):413–429.
  • Young P. The instrumental variable method: a practical approach to identification and parameter estimation. 7th IFAC/IFORS Symposium on Identification and System Parameter Estimation. 1985;18(5):1–15.

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