In this paper, we present and analyze a family of fifth-order iterative methods free from second derivative for solving nonlinear equations. It is established that the family of iterative methods has convergence order...In this paper, we present and analyze a family of fifth-order iterative methods free from second derivative for solving nonlinear equations. It is established that the family of iterative methods has convergence order five. Numerical examples show that the new methods are comparable with the well known existing methods and give better results in many aspects.展开更多
This study aims to investigate the polar decomposition of tensors with the Einstein product for thefirst time.The polar decomposition of tensors can be computed using the singular value decomposition of the tensors wit...This study aims to investigate the polar decomposition of tensors with the Einstein product for thefirst time.The polar decomposition of tensors can be computed using the singular value decomposition of the tensors with the Einstein product.In the following,some iterative methods forfinding the polar decomposi-tion of matrices have been developed into iterative methods to compute the polar decomposition of tensors.Then,we propose a novel parametric iterative method tofind the polar decomposition of tensors.Under the obtained conditions,we prove that the proposed parametric method has the order of convergence four.In every iteration of the proposed method,only four Einstein products are required,while other iterative methods need to calculate multiple Einstein products and one tensor inversion in each iteration.Thus,the new method is superior in terms of efficiency index.Finally,the numerical comparisons performed among several well-known methods,show that the proposed method is remarkably efficient and accurate.展开更多
In this paper, we establish two new iterative methods of order four and five by using modified homotopy perturbation technique. We also present the convergence analysis of these iterative methods. To assess the validi...In this paper, we establish two new iterative methods of order four and five by using modified homotopy perturbation technique. We also present the convergence analysis of these iterative methods. To assess the validity and performance of these iterative methods, we have applied to solve some nonlinear problems.展开更多
In the paper [1], authors have suggested and analyzed a predictor-corrector Halley method for solving nonlinear equations. In this paper, we modified this method by using the finite difference scheme, which had a quan...In the paper [1], authors have suggested and analyzed a predictor-corrector Halley method for solving nonlinear equations. In this paper, we modified this method by using the finite difference scheme, which had a quantic convergence. We have compared this modified Halley method with some other iterative methods of ninth order, which shows that this new proposed method is a robust one. Some examples are given to illustrate the efficiency and the performance of this new method.展开更多
There are several ways that can be used to classify or compare iterative methods for nonlinear equations,for instance;order of convergence,informational efficiency,and efficiency index.In this work,we use another way,...There are several ways that can be used to classify or compare iterative methods for nonlinear equations,for instance;order of convergence,informational efficiency,and efficiency index.In this work,we use another way,namely the basins of attraction of the method.The purpose of this study is to compare several iterative schemes for nonlinear equations.All the selected schemes are of the third-order of convergence and most of them have the same efficiency index.The comparison depends on the basins of attraction of the iterative techniques when applied on several polynomials of different degrees.As a comparison,we determine the CPU time(in seconds)needed by each scheme to obtain the basins of attraction,besides,we illustrate the area of convergence of these schemes by finding the number of convergent and divergent points in a selected range for all methods.Comparisons confirm the fact that basins of attraction differ for iterative methods of different orders,furthermore,they vary for iterative methods of the same order even if they have the same efficiency index.Consequently,this leads to the need for a new index that reflects the real efficiency of the iterative scheme instead of the commonly used efficiency index.展开更多
文摘In this paper, we present and analyze a family of fifth-order iterative methods free from second derivative for solving nonlinear equations. It is established that the family of iterative methods has convergence order five. Numerical examples show that the new methods are comparable with the well known existing methods and give better results in many aspects.
基金funded by Iran National Science Foundation(INSF)under project No.4013447.
文摘This study aims to investigate the polar decomposition of tensors with the Einstein product for thefirst time.The polar decomposition of tensors can be computed using the singular value decomposition of the tensors with the Einstein product.In the following,some iterative methods forfinding the polar decomposi-tion of matrices have been developed into iterative methods to compute the polar decomposition of tensors.Then,we propose a novel parametric iterative method tofind the polar decomposition of tensors.Under the obtained conditions,we prove that the proposed parametric method has the order of convergence four.In every iteration of the proposed method,only four Einstein products are required,while other iterative methods need to calculate multiple Einstein products and one tensor inversion in each iteration.Thus,the new method is superior in terms of efficiency index.Finally,the numerical comparisons performed among several well-known methods,show that the proposed method is remarkably efficient and accurate.
文摘In this paper, we establish two new iterative methods of order four and five by using modified homotopy perturbation technique. We also present the convergence analysis of these iterative methods. To assess the validity and performance of these iterative methods, we have applied to solve some nonlinear problems.
文摘In the paper [1], authors have suggested and analyzed a predictor-corrector Halley method for solving nonlinear equations. In this paper, we modified this method by using the finite difference scheme, which had a quantic convergence. We have compared this modified Halley method with some other iterative methods of ninth order, which shows that this new proposed method is a robust one. Some examples are given to illustrate the efficiency and the performance of this new method.
基金We are grateful for the financial support from UKM’s research Grant GUP-2019-033。
文摘There are several ways that can be used to classify or compare iterative methods for nonlinear equations,for instance;order of convergence,informational efficiency,and efficiency index.In this work,we use another way,namely the basins of attraction of the method.The purpose of this study is to compare several iterative schemes for nonlinear equations.All the selected schemes are of the third-order of convergence and most of them have the same efficiency index.The comparison depends on the basins of attraction of the iterative techniques when applied on several polynomials of different degrees.As a comparison,we determine the CPU time(in seconds)needed by each scheme to obtain the basins of attraction,besides,we illustrate the area of convergence of these schemes by finding the number of convergent and divergent points in a selected range for all methods.Comparisons confirm the fact that basins of attraction differ for iterative methods of different orders,furthermore,they vary for iterative methods of the same order even if they have the same efficiency index.Consequently,this leads to the need for a new index that reflects the real efficiency of the iterative scheme instead of the commonly used efficiency index.
