scholarly journals A New Approach for Solving Dual Fuzzy Nonlinear Equations Using Broyden's and Newton's Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
M. Y. Waziri ◽  
Z. A. Majid
Keyword(s):  
Nonlinear Equations ◽  
Newton's Method ◽  
Numerical Results ◽  
Parametric Form ◽  
New Approach ◽  
Broyden’S Method ◽  
Broyden's Method ◽  
Effectiveness And Efficiency ◽  
Initial Iteration ◽  
Newton's Methods

We present a new approach for solving dual fuzzy nonlinear equations. In this approach, we use Newton's method for initial iteration and Broyden's method for the rest of the iterations. The fuzzy coefficients are presented in parametric form. Numerical results on well-known benchmark fuzzy nonlinear equations are reported to authenticate the effectiveness and efficiency of the approach.

scholarly journals Chord Newton’s Method for Solving Fuzzy Nonlinear Equations

2019 ◽  
Vol 7 (1) ◽  
pp. 16
Author(s):  
Aliyu Usman Moyi
Keyword(s):  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Jacobian Matrix ◽  
Numerical Results ◽  
Parametric Form ◽  
New Approach ◽  
Effectiveness And Efficiency

In this paper, we present a new approach for solving fuzzy nonlinear equations. Our approach requires to  compute the Jacobian matrix once throughout the iterations unlike some Newton’s-like methods which needs to compute the Jacobian matrix in every iterations. The fuzzy coefficients are presented in parametric form. Numerical results on well-known benchmarks fuzzy nonlinear equations are reported to authenticate the effectiveness and efficiency of the approach.

scholarly journals Solving Dual Fuzzy Nonlinear Equations via Shamanskii Method

2018 ◽  
Vol 7 (3.28) ◽  
pp. 89 ◽  
Author(s):  
Ibrahim Mohammed Sulaiman ◽  
Mustafa Mamat ◽  
Nurnadiah Zamri ◽  
Puspa Liza Ghazali
Keyword(s):  
Numerical Methods ◽  
Numerical Method ◽  
Nonlinear Equations ◽  
Computational Cost ◽  
Numerical Results ◽  
Parametric Form ◽  
Solution Point ◽  
New Ideas

New ideas on numerical methods for solving fuzzy nonlinear equations have spread quickly across the globe. However, most of the methods available are based on Newton’s approach whose performance is impaired by either discontinuity or singularity of the Jacobian at the solution point. Also, the study of dual fuzzy nonlinear equations is yet to be explored by many researchers. Thus, in this paper, a numerical method to investigate the solution of dual fuzzy nonlinear equations is proposed. This method reduces the computational cost of Jacobian evaluation at every iteration. The fuzzy coefficients are presented in its parametric form. Numerical results obtained have shown that the proposed method is efficient. 

A Modification of Newton-Type Method with Sixth-Order Convergence for Solving Nonlinear Equations

2012 ◽  
Vol 490-495 ◽  
pp. 1839-1843
Author(s):  
Rui Chen ◽  
Liang Fang
Keyword(s):  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Efficiency Index ◽  
Numerical Results ◽  
Sixth Order ◽  
Order Convergence ◽  
Type Method ◽  
Second Derivatives ◽  
Better Than

In this paper, we present and analyze a modified Newton-type method with oder of convergence six for solving nonlinear equations. The method is free from second derivatives. It requires three evaluations of the functions and two evaluations of derivatives in each step. Therefore the efficiency index of the presented method is 1.431 which is better than that of classical Newton’s method 1.414. Some numerical results illustrate that the proposed method is more efficient and performs better than classical Newton's method

scholarly journals SOLVING DUAL FUZZY NONLINEAR EQUATIONS VIA MODIFIED STIRLING’S METHOD

2019 ◽  
Vol 4 (14) ◽  
pp. 84-91
Author(s):  
A. O Umar ◽  
M Mamat ◽  
M.Y Waziri
Keyword(s):  
Fixed Point ◽  
Nonlinear Equations ◽  
Unique Fixed Point ◽  
Numerical Results ◽  
Benchmark Problems ◽  
Parametric Form ◽  
Root Finding ◽  
Root Finding Method ◽  
Finding Method

Stirling’s method is a root-finding method designed to approximate a locally unique fixed point and cannot be used to solve fuzzy nonlinear equations. In this paper, we present a modified Stirling’s method for solving dual fuzzy nonlinear equations. The fuzzy coefficient is presented in parametric form. Numerical results on some benchmark problems indicate that the proposed method is efficient.

scholarly journals Global Convergence of Schubert’s Method for Solving Sparse Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Huiping Cao
Keyword(s):  
Global Convergence ◽  
Nonlinear Equations ◽  
Numerical Experiments ◽  
Large Scale ◽  
Line Search ◽  
Jacobian Matrix ◽  
Nonmonotone Line Search ◽  
Broyden’S Method ◽  
Large Scale Problems ◽  
Broyden's Method

Schubert’s method is an extension of Broyden’s method for solving sparse nonlinear equations, which can preserve the zero-nonzero structure defined by the sparse Jacobian matrix and can retain many good properties of Broyden’s method. In particular, Schubert’s method has been proved to be locally andq-superlinearly convergent. In this paper, we globalize Schubert’s method by using a nonmonotone line search. Under appropriate conditions, we show that the proposed algorithm converges globally and superlinearly. Some preliminary numerical experiments are presented, which demonstrate that our algorithm is effective for large-scale problems.

scholarly journals Broyden's Method for Solving Fuzzy Nonlinear Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-6 ◽  
Author(s):  
Amirah Ramli ◽  
Mohd Lazim Abdullah ◽  
Mustafa Mamat
Keyword(s):  
Nonlinear Equations ◽  
Fuzzy Number ◽  
Analytical Techniques ◽  
Numerical Examples ◽  
Broyden’S Method ◽  
Broyden's Method ◽  
Step Algorithm

Instead of using standard analytical techniques, like Buckley and Qu method, which are not suitable for solving a system of fuzzy nonlinear equations where the coefficient is fuzzy number, Broyden's method is proposed for solving fuzzy nonlinear equations. In this paper, an eight-step algorithm is used to solve fuzzy nonlinear equations. Two numerical examples are given to illustrate the proposed method.

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