Newton Method Research Papers - Academia.edu (original) (raw)

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An algorithm is described to estimate variance components for a univariate animal model using REML. Sparse matrix techniques are employed to calculate those elements of the inverse of the coefficient matrix required for the first... more

An algorithm is described to estimate variance components for a univariate animal model using REML. Sparse matrix techniques are employed to calculate those elements of the inverse of the coefficient matrix required for the first derivatives of the likelihood. Residuals and fitted ...

In this paper, we have combined the ideas of the False Position (FP) and Artificial Bee Colony (ABC) algorithms to find a fast and novel method for solving nonlinear equations. Additionally, to illustrate the efficiency of the proposed... more

In this paper, we have combined the ideas of the False Position (FP) and Artificial Bee Colony (ABC) algorithms to find a fast and novel method for solving nonlinear equations. Additionally, to illustrate the efficiency of the proposed method, several benchmark functions are solved and compared with other methods such as ABC, PSO and GA.

Ini adalah Program Interpolasi Newton dan Lagrange dengan menggunakan MATLAB

Three issues concerning the iterative solution of the nonlinear equations governing the flows and heads in a water distribution system network are considered. Zero flows cause a computation failure (division by zero) when the Global... more

Three issues concerning the iterative solution of the nonlinear equations governing the flows and heads in a water distribution system network are considered. Zero flows cause a computation failure (division by zero) when the Global Gradient Algorithm of Todini and Pilati is used to solve for the steady state of a system in which the head loss is modeled by the Hazen-Williams formula. The proposed regularization technique overcomes this failure as a solution to this first issue. The second issue relates to zero flows in the Darcy-Weisbach formulation. This work explains for the first time why zero flows do not lead to a division by zero where the head loss is modeled by the Darcy-Weisbach formula. In this paper, the authors show how to handle the computation appropriately in the case of laminar flow (the only instance in which zero flows may occur). However, as is shown, a significant loss of accuracy can result if the Jacobian matrix, necessary for the solution process, becomes poorly conditioned, and so it is recommended that the regularization technique be used for the Darcy-Weisbach case also. Only a modest extra computational cost is incurred when the technique is applied. The third issue relates to a new convergence stopping criterion for the iterative process based on the infinity-norm of the vector of nodal head differences between one iteration and the next. This test is recommended because it has a more natural physical interpretation than the relative discharge stopping criterion that is currently used in standard software packages such as EPANET. In addition, it is recommended to check the infinity norms of the residuals once iteration has been stopped. The residuals test ensures that inaccurate solutions are not accepted.

The new second-order and third-order iterative methods without derivatives are presented for solving nonlinear equations; the iterative formulae based on the homotopy perturbation method are deduced and their convergences are provided.... more

The new second-order and third-order iterative methods without derivatives are presented for solving nonlinear equations; the iterative formulae based on the homotopy perturbation method are deduced and their convergences are provided. Finally, some numerical experiments show the efficiency of the theoretical results for the above methods.

A new method for the solution of minimization problems with simple bounds is presented. Global convergence of a general scheme requiring the approximate solution of a single linear system at each iteration is proved and a superlinear... more

A new method for the solution of minimization problems with simple bounds is presented. Global convergence of a general scheme requiring the approximate solution of a single linear system at each iteration is proved and a superlinear convergence rate is established without requiring the strict complementarity assumption. The algorithm pro- posed is based on a simple, smooth unconstrained reformulation of

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