Convergence and uniqueness properties of Gauss-Newton's method

Li, Chong; Zhang, Wenhong; Jin, Xiaoqing

doi:10.1016/s0898-1221(04)90086-7

Cited by 44 publications

(47 citation statements)

References 5 publications

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“…instead of the stronger hypotheses (1.4) used in [8], leads us to the advantages as stated in the abstract of this study of our approach over the corressponding ones in [8].…”

Section: Introductionmentioning

confidence: 88%

“…is a closed set), and Hence, we have expanded with applicability of Gauss-Newton method (1.3) under the same computational cost and with a smaller ratio than in [8].…”

Section: It Follows From the Intermediate Value Theorem That There Exmentioning

confidence: 99%

“…Using more precise estimates on the distances involved, under weaker hypotheses, and under the same computational cost, we provide an analysis of the GaussNewton method with the following advantages over the corresponding results in [8]: larger convergence domain; finer error estimates on the distances involved, and an at least as precise information on the location of the solution AMS Subject Classification. 65F20, 65G99, 65H10, 49M15.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, in the case of Gauss-Newton method (1.3), Li et al provided a semilocal convergence analysis in [8] using the concept of the Lipschitz condition.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, we provide a semilocal convergence analysis with the following advantages over the work by Li et al [8]:…”

Section: Introductionmentioning

confidence: 99%

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On the Gauss-Newton method for solving equations

Argyros

Hitlout

2012

Proyecciones (Antofagasta)

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We use a combination of the center-Lipschitz condition with the Lipschitz condition condition on the Fréchet-derivative of the operator involved to provide a semilocal convergence analysis of the GaussNewton method to a solution of an equation. Using more precise estimates on the distances involved, under weaker hypotheses, and under the same computational cost, we provide an analysis of the GaussNewton method with the following advantages over the corresponding results in [8]: larger convergence domain; finer error estimates on the distances involved, and an at least as precise information on the location of the solution AMS Subject Classification. 65F20, 65G99, 65H10, 49M15.

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“…instead of the stronger hypotheses (1.4) used in [8], leads us to the advantages as stated in the abstract of this study of our approach over the corressponding ones in [8].…”

Section: Introductionmentioning

confidence: 88%

“…is a closed set), and Hence, we have expanded with applicability of Gauss-Newton method (1.3) under the same computational cost and with a smaller ratio than in [8].…”

Section: It Follows From the Intermediate Value Theorem That There Exmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In particular, in the case of Gauss-Newton method (1.3), Li et al provided a semilocal convergence analysis in [8] using the concept of the Lipschitz condition.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, we provide a semilocal convergence analysis with the following advantages over the work by Li et al [8]:…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On the Gauss-Newton method for solving equations

Argyros

Hitlout

2012

Proyecciones (Antofagasta)

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Newton’s Method for Convex Optimization

Argyros

González

2016

SEMA SIMAI Springer Series

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Newton’s Method and Secant Method for Set-Valued Mappings

Baier

Molo

2012

Large-Scale Scientific Computing

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For finding zeros or fixed points of set-valued maps, the fact that the space of convex, compact, nonempty sets of R n is not a vector space presents a major disadvantage. Therefore, fixed point iterations or variants of Newton's method, in which the derivative is applied only to a smooth single-valued part of the set-valued map, are often applied for calculations. We will embed the set-valued map with convex, compact images (i.e. by embedding its images) and shift the problem to the Banach space of directed sets. This Banach space extends the arithmetic operations of convex sets and allows to consider the Fréchet-derivative or divided differences of maps that have embedded convex images. For the transformed problem, Newton's method and the secant method in Banach spaces are applied via directed sets. The results can be visualized as usually nonconvex sets in R n .

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Convergence and uniqueness properties of Gauss-Newton's method

Cited by 44 publications

References 5 publications

On the Gauss-Newton method for solving equations

On the Gauss-Newton method for solving equations

Newton’s Method for Convex Optimization

Newton’s Method and Secant Method for Set-Valued Mappings

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