New modification of Maheshwari’s method with optimal eighth order convergence for solving nonlinear equations

Somayeh Sharifi; Massimiliano Ferrara; Mehdi Salimi; Stefan Siegmund

Displaying similar documents to “New modification of Maheshwari’s method with optimal eighth order convergence for solving nonlinear equations”

On a high-order iterative scheme for a nonlinear Love equation

Le Thi Phuong Ngoc, Nguyen Tuan Duy, Nguyen Thanh Long (2015)

Applications of Mathematics

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In this paper, a high-order iterative scheme is established for a nonlinear Love equation associated with homogeneous Dirichlet boundary conditions. This is a development based on recent results (L. T. P. Ngoc, N. T. Long (2011); L. X. Truong, L. T. P. Ngoc, N. T. Long (2009)) to get a convergent sequence at a rate of order $N \geq 2$ to a local unique weak solution of the above mentioned equation.

A new optimized iterative method for solving $M$ -matrix linear systems

Alireza Fakharzadeh Jahromi, Nafiseh Nasseri Shams (2022)

Applications of Mathematics

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In this paper, we present a new iterative method for solving a linear system, whose coefficient matrix is an $M$ -matrix. This method includes four parameters that are obtained by the accelerated overrelaxation (AOR) splitting and using the Taylor approximation. First, under some standard assumptions, we establish the convergence properties of the new method. Then, by minimizing the Frobenius norm of the iteration matrix, we find the optimal parameters. Meanwhile, numerical results on test...

Newton-type iterative methods for nonlinear ill-posed Hammerstein-type equations

Monnanda Erappa Shobha, Ioannis K. Argyros, Santhosh George (2014)

Applicationes Mathematicae

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We use a combination of modified Newton method and Tikhonov regularization to obtain a stable approximate solution for nonlinear ill-posed Hammerstein-type operator equations KF(x) = y. It is assumed that the available data is $y^{δ}$ with $| | y - y^{δ} | | \leq δ$ , K: Z → Y is a bounded linear operator and F: X → Z is a nonlinear operator where X,Y,Z are Hilbert spaces. Two cases of F are considered: where $F^{'} {(x ₀)}^{- 1}$ exists (F’(x₀) is the Fréchet derivative of F at an initial guess x₀) and where F is a monotone operator....

The use of basic iterative methods for bounding a solution of a system of linear equations with an M-matrix and positive right-hand side

Kocurek, Martin

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This article presents a simple method for bounding a solution of a system of linear equations $A x = b$ with an M-matrix and positive right-hand side [1]. Given a suitable approximation to an exact solution, the bounds are constructed by one step in a basic iterative method.

A convergent nonlinear splitting via orthogonal projection

Jan Mandel (1984)

Aplikace matematiky

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We study the convergence of the iterations in a Hilbert space $V, x_{k + 1} = W (P) x_{k}, W (P) z = w = T (P w + (I - P) z)$ , where $T$ maps $V$ into itself and $P$ is a linear projection operator. The iterations converge to the unique fixed point of $T$ , if the operator $W (P)$ is continuous and the Lipschitz constant $∥(I - P) W (P)∥ < 1$ . If an operator $W (P_{1})$ satisfies these assumptions and $P_{2}$ is an orthogonal projection such that $P_{1} P_{2} = P_{2} P_{1} = P_{1}$ , then the operator $W (P_{2})$ is defined and continuous in $V$ and satisfies $∥(I - P_{2}) W (P_{2})∥ \leq ∥(I - P_{1}) W (P_{1})∥$ .

On the convergence theory of double $K$ -weak splittings of type II

Vaibhav Shekhar, Nachiketa Mishra, Debasisha Mishra (2022)

Applications of Mathematics

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Recently, Wang (2017) has introduced the $K$ -nonnegative double splitting using the notion of matrices that leave a cone $K \subseteq ℝ^{n}$ invariant and studied its convergence theory by generalizing the corresponding results for the nonnegative double splitting by Song and Song (2011). However, the convergence theory for $K$ -weak regular and $K$ -nonnegative double splittings of type II is not yet studied. In this article, we first introduce this class of splittings and then discuss the convergence theory...

Complete $f$ -moment convergence for weighted sums of WOD arrays with statistical applications

Xi Chen, Xinran Tao, Xuejun Wang (2023)

Kybernetika

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Complete $f$ -moment convergence is much more general than complete convergence and complete moment convergence. In this work, we mainly investigate the complete $f$ -moment convergence for weighted sums of widely orthant dependent (WOD, for short) arrays. A general result on Complete $f$ -moment convergence is obtained under some suitable conditions, which generalizes the corresponding one in the literature. As an application, we establish the complete consistency for the weighted linear estimator...

A dual-parameter double-step splitting iteration method for solving complex symmetric linear equations

Beibei Li, Jingjing Cui, Zhengge Huang, Xiaofeng Xie (2024)

Applications of Mathematics

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We multiply both sides of the complex symmetric linear system $A x = b$ by $1 - i ω$ to obtain a new equivalent linear system, then a dual-parameter double-step splitting (DDSS) method is established for solving the new linear system. In addition, we present an upper bound for the spectral radius of iteration matrix of the DDSS method and obtain its quasi-optimal parameter. Theoretical analyses demonstrate that the new method is convergent when some conditions are satisfied. Some tested examples are...

The new iteration methods for solving absolute value equations

Rashid Ali, Kejia Pan (2023)

Applications of Mathematics

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Many problems in operations research, management science, and engineering fields lead to the solution of absolute value equations. In this study, we propose two new iteration methods for solving absolute value equations $A x - | x | = b$ , where $A \in ℝ^{n \times n}$ is an $M$ -matrix or strictly diagonally dominant matrix, $b \in ℝ^{n}$ and $x \in ℝ^{n}$ is an unknown solution vector. Furthermore, we discuss the convergence of the proposed two methods under suitable assumptions. Numerical experiments are given to verify the feasibility, robustness...