scholarly journals On an application of Herzberger’s matrix method to multipoint families of root-solvers

Filomat ◽  
2018 ◽  
Vol 32 (11) ◽  
pp. 3815-3829 ◽  
Author(s):  
Jovana Dzunic ◽  
Ljiljana Petkovic ◽  
Miodrag Petkovic
Keyword(s):  
Nonlinear Equations ◽  
Matrix Method ◽  
Order Of Convergence ◽  
Multipoint Methods ◽  
S Matrix ◽  
Area Of Application

An application of Herzberger?s matrix method, very rarely used in the topic of multipoint methods for solving nonlinear equations, is presented. It is shown that the area of application of Herzberger?s matrix method is wider than it is presented in [J. Herzberger, ?ber Matrixdarstellungen f?r Iterationverfahren bei nichtlinearen Gleichungen, Computing, 12 (1974) 215-222]. This method is applied for the determination of the order of convergence of multipoint families of methods, Steffensen?s type and Newton?s type, with and without memory. The advantage and the elegance of this method arise from ease in handling matrices.

S-Matrix Method for the Numerical Determination of Bound States

1973 ◽  
Vol 7 (2) ◽  
pp. 523-525 ◽  
Author(s):  
A. K. Bhatia ◽  
R. N. Madan
Keyword(s):  
Matrix Method ◽  
Bound States ◽  
Numerical Determination ◽  
S Matrix

scholarly journals On Some Iterative Methods with Memory and High Efficiency Index for Solving Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Tahereh Eftekhari
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
High Efficiency ◽  
Efficiency Index ◽  
Order Convergence ◽  
Eighth Order ◽  
Additional Function ◽  
Numerical Comparisons ◽  
With Memory

Based on iterative methods without memory of eighth-order convergence proposed by Thukral (2012), some iterative methods with memory and high efficiency index are presented. We show that the order of convergence is increased without any additional function evaluations. Numerical comparisons are made to show the performance of the presented methods.

Determination of the Force Constants of Non-linear XY2 Molecules in the Gas-Phase by the GF Matrix Method

2004 ◽  
Vol 59 (9) ◽  
pp. 621-622 ◽  
Author(s):  
Fatih Ucun ◽  
Vesile Gūçlü
Keyword(s):  
Gas Phase ◽  
Condensed Phase ◽  
Matrix Method ◽  
Solid Phase ◽  
Force Constants ◽  
Matrix Solution ◽  
The Matrix ◽  
Newton Raphson ◽  
Raphson Method

The force constants of the internal coordinates of nonlinear XY2 molecules in the gas-phase were calculated by using the GF matrix method. The matrix solution was carried out by means a computer program built relative to the Newton-Raphson method and the calculations were listed in a table. The force constants of some molecules in the liquidand solid- phase were also found and compared with these ones, and it was seen that the force constants for more condensed phase are lower as in an agreement with having its lower frequency.

scholarly journals On a Derivative-Free Variant of King’s Family with Memory

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
M. Sharifi ◽  
S. Karimi Vanani ◽  
F. Khaksar Haghani ◽  
M. Arab ◽  
S. Shateyi
Keyword(s):  
Nonlinear Equations ◽  
Numerical Experiments ◽  
Order Of Convergence ◽  
Derivative Free ◽  
With Memory

The aim of this paper is to construct a method with memory according to King’s family of methods without memory for nonlinear equations. It is proved that the proposed method possesses higherR-order of convergence using the same number of functional evaluations as King’s family. Numerical experiments are given to illustrate the performance of the constructed scheme.

scholarly journals Metode Iterasi Tiga Langkah untuk Menyelesaikan Persamaan NonLinear dengan Menggunakan Matlab

2019 ◽  
Vol 4 (2) ◽  
pp. 34
Author(s):  
Deasy Wahyuni ◽  
Elisawati Elisawati
Keyword(s):  
Numerical Simulations ◽  
Nonlinear Equations ◽  
Newton Method ◽  
Iteration Method ◽  
Newton's Method ◽  
Order Of Convergence ◽  
Higher Order ◽  
Convergence Order ◽  
Matlab Program ◽  
Analytical Results

Newton method is one of the most frequently used methods to find solutions to the roots of nonlinear equations. Along with the development of science, Newton's method has undergone various modifications. One of them is the hasanov method and the newton method variant (vmn), with a higher order of convergence. In this journal focuses on the three-step iteration method in which the order of convergence is higher than the three methods. To find the convergence order of the three-step iteration method requires a program that can support the analytical results of both methods. One of them using the help of the matlab program. Which will then be compared with numerical simulations also using the matlab program.  Keywords : newton method, newton method variant, Hasanov Method and order of convergence

Determination of the effective permittivity of dielectric mixtures with the transmission line matrix method

2007 ◽  
Vol 102 (6) ◽  
pp. 064101 ◽  
Author(s):  
Cédric Blanchard ◽  
Jorge A. Portí ◽  
Juan A. Morente ◽  
Alfonso Salinas ◽  
Enrique A. Navarro
Keyword(s):  
Transmission Line ◽  
Matrix Method ◽  
Effective Permittivity ◽  
Transmission Line Matrix

Transfer Matrix Eigensolutions for Damped Torsional Systems

1985 ◽  
Vol 107 (1) ◽  
pp. 128-132 ◽  
Author(s):  
S. Doughty ◽  
G. Vafaee
Keyword(s):  
General Solution ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Solution Method ◽  
The Other ◽  
Torsional Vibrations

A transfer matrix method is presented for the determination of complex eigensolutions associated with the damped torsional vibrations of single shaft machine trains. The system is described and the natures of the eigenvalues are discussed. The general solution method is developed, and the method is applied to two example problems. One of the examples is quite simple, while the other is entirely realistic.

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