Numerical solution of nonlinear equations by an optimal eighth-order class of iterative methods

Soleymani, Fazlollah; Vanani, S. Karimi; Siyyam, Hani I.; Al-Subaihi, I. A.

doi:10.1007/s11565-012-0165-5

Cited by 7 publications

(5 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The derivation of different Schulz-type methods for matrix inversion relies on iterative (one-or multipoint) methods for the solution of nonlinear equations [19,20]. For instance, imposing Newton's iteration on the matrix equation = would result in (1), as fully discussed in [21].…”

Section: Resultsmentioning

confidence: 99%

Approximating the Inverse of a Square Matrix with Application in Computation of the Moore-Penrose Inverse

Soleymani¹,

Sharifi²,

Shateyi

2014

Journal of Applied Mathematics

View full text Add to dashboard Cite

This paper presents a computational iterative method to find approximate inverses for the inverse of matrices. Analysis of convergence reveals that the method reaches ninth-order convergence. The extension of the proposed iterative method for computing Moore-Penrose inverse is furnished. Numerical results including the comparisons with different existing methods of the same type in the literature will also be presented to manifest the superiority of the new algorithm in finding approximate inverses. +1 to keep the approximated inverse sparse. Such a strategy is useful for preconditioning.

show abstract

Section: Resultsmentioning

confidence: 99%

Approximating the Inverse of a Square Matrix with Application in Computation of the Moore-Penrose Inverse

Soleymani¹,

Sharifi²,

Shateyi

2014

Journal of Applied Mathematics

View full text Add to dashboard Cite

show abstract

“…The other context is in solving nonlinear algebraic system of equations. As a matter of fact, when it comes to a system of equations, the order optimality (as discussed by Kung-Traub-1974 for iteration schemes without memory [3]) cannot be achieved anymore. In such cases, the lower the computational cost of computing Jacobians/Hessian matrices, the more useful the method is; see [4] for more information.…”

Section: Introduction and The Fractal Behavior Of Iteration Methodsmentioning

confidence: 99%

From Fractal Behavior of Iteration Methods to an Efficient Solver for the Sign of a Matrix

et al. 2022

View full text Add to dashboard Cite

Investigating the fractal behavior of iteration methods on special polynomials can help to find iterative methods with global convergence for finding special matrix functions. By employing such a methodology, we propose a new solver for the sign of an invertible square matrix. The presented method achieves the fourth rate of convergence by using as few matrix products as possible. Its attraction basin shows larger convergence radii, in contrast to its Padé-type methods of the same order. Computational tests are performed to check the efficacy of the proposed solver.

show abstract

“…To do this, the development in Taylor series is done in the neighborhood of the function f(y n ), for which the equation (14) is important because it represents an approximation to the zero of the function. Then, developing in Taylor series f(y n ), in the neighborhood of d n , we have equation (15).…”

Section: The Methods and Analysis Of Convergencementioning

confidence: 99%

“…Thus, different authors have proposed high-order, multi-step methods to solve a real nonlinear equation, all with the aim of increasing efficiency [15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

An Iterative Method to Solve Nonlinear Equations

Villafuerte¹,

Medina²,

Villafuerte³

et al. 2019

ujeee

View full text Add to dashboard Cite

In this paper, an iterative Newton-type method of three steps and fourth order is applied to solve the nonlinear equations that model the load flow in electric power systems. With the proposed method (N-1) non-linear equations are formulated and solved iteratively to calculate the Voltage in each node of an electrical system. The justification of the method and its theoretical preliminaries are presented in this paper. The proposed method is applied to IEEE test systems, and their results are compared obtaining a maximum error of 0.5%. From the results obtained, the proposed method is an alternative to solve load flows in electrical systems.

show abstract

Numerical solution of nonlinear equations by an optimal eighth-order class of iterative methods

Cited by 7 publications

References 17 publications

Approximating the Inverse of a Square Matrix with Application in Computation of the Moore-Penrose Inverse

Approximating the Inverse of a Square Matrix with Application in Computation of the Moore-Penrose Inverse

From Fractal Behavior of Iteration Methods to an Efficient Solver for the Sign of a Matrix

An Iterative Method to Solve Nonlinear Equations

Contact Info

Product

Resources

About