2011
DOI: 10.1007/s11075-011-9446-9
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Abstract: We extend the applicability of the Gauss-Newton method for solving singular systems of equations under the notions of average Lipschitz-type conditions introduced recently in Li et al. (J Complex 26(3):268-295, 2010). Using our idea of recurrent functions, we provide a tighter local as well as semilocal convergence analysis for the Gauss-Newton method than in Li et al. (J Complex 26(3):268-295, 2010) who recently extended and improved earlier results (Hu et al. ). We also note that our results are obtained und… Show more

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Cited by 25 publications
(28 citation statements)
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“…The advantages of our analysis over earlier works such as [8,9,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43] are also shown under the same computational cost for the functions and constants involved. These advantages include: a large radius of convergence and more precise error estimates on the distances x n+1 − x * for each n = 0, 1, 2, .…”
Section: Resultsmentioning
confidence: 74%
See 1 more Smart Citation
“…The advantages of our analysis over earlier works such as [8,9,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43] are also shown under the same computational cost for the functions and constants involved. These advantages include: a large radius of convergence and more precise error estimates on the distances x n+1 − x * for each n = 0, 1, 2, .…”
Section: Resultsmentioning
confidence: 74%
“…Suppose that µ(µ 1 + µ 2 ) < 1. Then, Q(x) = 0 has three distinct and positive solutions defined by Other examples can be found in [2,8,5,10,12].…”
Section: Numerical Examplesmentioning
confidence: 99%
“…Under the hypothesis that F (x )F satisfies certain Lipschitz conditions, we presented a more precise local convergence analysis for the inexact GaussNewton method under the same computational cost as in earlier studies such as [3,4,[6][7][8]11] with advantages as stated in the abstract of this paper using our new idea of restricted convergence domains. Numerical examples are provided to show these advantages.…”
Section: Discussionmentioning
confidence: 99%
“…Estimate (2.9) holds as a strict inequality. Therefore, the new error bounds are more precise than the old ones using only L 1 [7][8][9] or L 0 and L 1 [4,5].…”
Section: Applications and Examplesmentioning
confidence: 90%
“…. , where x 0 ∈ D is an initial point and F ′ (x n ) + is the Moore-Penrose inverse of the linear operator F ′ (x n ) [7,9,12,14,16,18]. In the present paper we use the proximal Gauss-Newton method (to be precised in Section 2, see (2.6)) for solving penalized nonlinear least squares problem (1.1).…”
Section: Introductionmentioning
confidence: 99%