A new truncated-perturbed Gauss–Newton method for underdetermined nonlinear least squares problems

References

• Argyros IK, Szidarovszky F. The theory and applications of iteration methods. Boca Raton, FL: CRC Press; 1993.
   Google Scholar
• Gratton S, Lawless AS, Nichols NK. Approximate Gauss–Newton methods for nonlinear least squares problems. SIAM J Optim. 2007;18(1):106–132. doi: 10.1137/050624935
   Web of Science ®Google Scholar
• Ortega JM, Rheinboldt WC. Iterative solution of nonlinear equations in several variables. Vol. 30. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM); 2000. (Classics in Applied Mathematics). pp. xxvi+572. Reprint of the 1970 original.
   Google Scholar
• Kim S, Tewarson RP. The convergence of quasi-Gauss-Newton methods for nonlinear problems. Comput Math Appl. 1995;29(8):27–38. doi: 10.1016/0898-1221(95)00027-V
   Web of Science ®Google Scholar
• Gonçalves MLN. Local convergence of the Gauss-Newton method for injective-overdetermined systems of equations under a majorant condition. Comput Math Appl. 2013;66(4):490–499. doi: 10.1016/j.camwa.2013.05.019
   Web of Science ®Google Scholar
• Bao J, Yu CKW, Wang J, et al. Modified inexact Levenberg-Marquardt methods for solving nonlinear least squares problems. Comput Optim Appl. 2019;74(2):547–582. doi: 10.1007/s10589-019-00111-y
   Web of Science ®Google Scholar
• Bellavia S, Gratton S, Riccietti E. A Levenberg-Marquardt method for large nonlinear least-squares problems with dynamic accuracy in functions and gradients. Numer Math. 2018;140(3):791–825. doi: 10.1007/s00211-018-0977-z
   Web of Science ®Google Scholar
• Fasano G, Lampariello F, Sciandrone M. A truncated nonmonotone Gauss-Newton method for large-scale nonlinear least-squares problems. Comput Optim Appl. 2006;34(3):343–358. doi: 10.1007/s10589-006-6444-2
   Web of Science ®Google Scholar
• Li C, Zhang WH, Jin XQ. Convergence and uniqueness properties of Gauss-Newton's method. Comput Math Appl. 2004;47(6-7):1057–1067. doi: 10.1016/S0898-1221(04)90086-7
   Web of Science ®Google Scholar
• Shakhno SM. Gauss-Newton-Kurchatov method for the solution of nonlinear least-squares problems. J Math Sci (N.Y.). 2020;247(1):58–72. doi: 10.1007/s10958-020-04789-y
   Google Scholar
• Xu C. Nonlinear least squares: Newton-type methods. Boston, MA: Springer US; 2001. pp. 1739–1745.
   Google Scholar
• Björck Å. Numerical methods for least squares problems. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM); 1996.
   Google Scholar
• Bao JF, Li C, Shen WP, et al. Approximate Gauss-Newton methods for solving underdetermined nonlinear least squares problems. Appl Numer Math. 2017;111:92–110. doi: 10.1016/j.apnum.2016.08.007
   Web of Science ®Google Scholar
• Rokne J. Newton's method under mild differentiability conditions with error analysis. Numer Math. 1971;18(5):401–412. doi: 10.1007/BF01406677
   Web of Science ®Google Scholar
• Ortega JM. Numerical analysis. Vol. 3. 2nd ed., Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM); 1990. (Classics in Applied Mathematics). pp. xiv+201. A second course.
   Google Scholar
• Keller HB. Newton's method under mild differentiability conditions. J Comput Syst Sci. 1970;4:15–28. doi: 10.1016/S0022-0000(70)80009-5
   Google Scholar
• Argyros IK, Hilout S. On the convergence of Newton-type methods under mild differentiability conditions. Numer Algorithms. 2009;52(4):701–726. doi: 10.1007/s11075-009-9308-x
   Web of Science ®Google Scholar
• Moré JJ, Garbow BS, Hillstrom KE. Testing unconstrained optimization software. ACM Trans Math Softw. 1981;7(1):17–41. doi: 10.1145/355934.355936
   Web of Science ®Google Scholar
• Dan H, Yamashita N, Fukushima M. Convergence properties of the inexact Levenberg-Marquardt method under local error bound conditions. Optim Methods Softw. 2002;17(4):605–626. doi: 10.1080/1055678021000049345
   Web of Science ®Google Scholar
• La Cruz W, Raydan M. Nonmonotone spectral methods for large-scale nonlinear systems. Optim Methods Softw. 2003;18(5):583–599. doi: 10.1080/10556780310001610493
   Web of Science ®Google Scholar