Semilocal convergence of multi-point improved super-Halley-type methods without the second derivative under generalized weak condition

2015 ◽  
Vol 71 (3) ◽  
pp. 567-584 ◽  
Author(s):  
Xiuhua Wang ◽  
Jisheng Kou
Keyword(s):  
Semilocal Convergence ◽  
Weak Condition ◽  
Second Derivative

scholarly journals Analysis of semilocal convergence for ameliorated super-Halley methods with less computation for inversion

2016 ◽  
Vol 19 (1) ◽  
pp. 293-302
Author(s):  
Xiuhua Wang ◽  
Jisheng Kou
Keyword(s):  
Uniqueness Theorem ◽  
Banach Spaces ◽  
Semilocal Convergence ◽  
Second Derivative

In this paper, the semilocal convergence for ameliorated super-Halley methods in Banach spaces is considered. Different from the results in [J. M. Gutiérrez and M. A. Hernández, Comput. Math. Appl. 36 (1998) 1–8], these ameliorated methods do not need to compute a second derivative, the computation for inversion is reduced and the $R$-order is also heightened. Under a weaker condition, an existence–uniqueness theorem for the solution is proved.

Semilocal Convergence Theorem for a Newton-like Method

2017 ◽  
Vol 7 (3) ◽  
pp. 482-494
Author(s):  
Rong-Fei Lin ◽  
Qing-Biao Wu ◽  
Min-Hong Chen ◽  
Lu Liu ◽  
Ping-Fei Dai
Keyword(s):  
Error Estimate ◽  
Nonlinear Equations ◽  
Convergence Theorem ◽  
Nonlinear Operator ◽  
Semilocal Convergence ◽  
Weak Condition ◽  
Third Order ◽  
Convergence Theorems ◽  
Numerical Examples ◽  
Semilocal Convergence Theorem

AbstractThe semilocal convergence of a third-order Newton-like method for solving nonlinear equations is considered. Under a weak condition (the so-called γ-condition) on the derivative of the nonlinear operator, we establish a new semilocal convergence theorem for the Newton-like method and also provide an error estimate. Some numerical examples show the applicability and efficiency of our result, in comparison to other semilocal convergence theorems.

scholarly journals Semilocal Convergence Analysis for Inexact Newton Method under Weak Condition

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Xiubin Xu ◽  
Yuan Xiao ◽  
Tao Liu
Keyword(s):  
Newton Method ◽  
Convergence Theorem ◽  
Semilocal Convergence ◽  
Weak Condition ◽  
Inexact Newton Method ◽  
Convergence Criteria ◽  
First Derivative ◽  
Special Cases ◽  
Lipschitz Conditions ◽  
Semilocal Convergence Theorem

Under the hypothesis that the first derivative satisfies some kind of weak Lipschitz conditions, a new semilocal convergence theorem for inexact Newton method is presented. Unified convergence criteria ensuring the convergence of inexact Newton method are also established. Applications to some special cases such as the Kantorovich type conditions andγ-Conditions are provided and some well-known convergence theorems for Newton's method are obtained as corollaries.

scholarly journals On semilocal convergence of three-step Kurchatov method under weak condition

2021 ◽  
Author(s):  
Himanshu Kumar
Keyword(s):  
Recurrence Relations ◽  
Divided Difference ◽  
Semilocal Convergence ◽  
Weak Condition ◽  
Theoretical Development ◽  
Difference Operators ◽  
Nonlinear System Of Equations ◽  
First Order ◽  
Type Integral ◽  
Weaker Conditions

AbstractThe purpose of this paper to establish the semilocal convergence analysis of three-step Kurchatov method under weaker conditions in Banach spaces. We construct the recurrence relations under the assumption that involved first-order divided difference operators satisfy the $$\omega $$ ω condition. Theorems are given for the existence-uniqueness balls enclosing the unique solution. The application of the iterative method is shown by solving nonlinear system of equations and nonlinear Hammerstein-type integral equations. It illustrates the theoretical development of this study.

Second‐Derivative Spectra for Estimating Crop Residue Cover

1994 ◽  
Vol 86 (2) ◽  
pp. 349-354 ◽  
Author(s):  
Haiping Su ◽  
Michel D. Ransom ◽  
Edward T. Kanemasu ◽  
Tanvir H. Demetriades‐Shah
Keyword(s):  
Crop Residue ◽  
Second Derivative ◽  
Derivative Spectra ◽  
Second Derivative Spectra

Earth's gravity field parameters determination by the space geodesy dynamical approach

2017 ◽  
Vol 919 (1) ◽  
pp. 7-12
Author(s):  
N.A Sorokin
Keyword(s):  
Coordinate System ◽  
Gravitational Potential ◽  
Coefficient Matrix ◽  
Measured Quantity ◽  
Second Derivative ◽  
Measured Variable ◽  
Second Derivatives ◽  
Rectangular Coordinates ◽  
Cartesian Coordinate ◽  
Derivatives Of

The method of the geopotential parameters determination with the use of the gradiometry data is considered. The second derivative of the gravitational potential in the correction equation on the rectangular coordinates x, y, z is used as a measured variable. For the calculated value of the measured quantity required for the formation of a free member of the correction equation, the the Cunningham polynomials were used. We give algorithms for computing the second derivatives of the Cunningham polynomials on rectangular coordinates x, y, z, which allow to calculate the second derivatives of the geopotential at the rectangular coordinates x, y, z.Then we convert derivatives obtained from the Cartesian coordinate system in the coordinate system of the gradiometer, which allow to calculate the free term of the correction equation. Afterwards the correction equation coefficients are calculated by differentiating the formula for calculating the second derivative of the gravitational potential on the rectangular coordinates x, y, z. The result is a coefficient matrix of the correction equations and corrections vector of the free members of equations for each component of the tensor of the geopotential. As the number of conditional equations is much more than the number of the specified parameters, we go to the drawing up of the system of normal equations, from which solutions we determine the required corrections to the harmonic coefficients.

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