scholarly journals A New High-Order Stable Numerical Method for Matrix Inversion

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
F. Khaksar Haghani ◽  
F. Soleymani
Keyword(s):  
Iterative Method ◽  
Numerical Method ◽  
Matrix Inversion ◽  
High Order ◽  
New Method ◽  
Order Convergence ◽  
Initial Value ◽  
Numerical Examples ◽  
Stable Numerical Method

A stable numerical method is proposed for matrix inversion. The new method is accompanied by theoretical proof to illustrate twelfth-order convergence. A discussion of how to achieve the convergence using an appropriate initial value is presented. The application of the new scheme for finding Moore-Penrose inverse will also be pointed out analytically. The efficiency of the contributed iterative method is clarified on solving some numerical examples.

An Accelerated Iterative Method with Third-Order Convergence

2012 ◽  
Vol 220-223 ◽  
pp. 2658-2661
Author(s):  
Zhong Yong Hu ◽  
Liang Fang ◽  
Lian Zhong Li
Keyword(s):  
Iterative Method ◽  
Fourth Order ◽  
Newton’S Method ◽  
Newton's Method ◽  
New Method ◽  
Order Convergence ◽  
Third Order ◽  
Numerical Examples ◽  
Modified Newton’S Method ◽  
Jarratt Method

We present a new modified Newton's method with third-order convergence and compare it with the Jarratt method, which is of fourth-order. Based on this new method, we obtain a family of Newton-type methods, which converge cubically. Numerical examples show that the presented method can compete with Newton's method and other known third-order modifications of Newton's method.

scholarly journals A High-Order Iterate Method for ComputingAT,S(2)

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Xiaoji Liu ◽  
Zemeng Zuo
Keyword(s):  
Iterative Method ◽  
Generalized Inverse ◽  
Higher Order ◽  
High Order ◽  
New Method ◽  
Order Convergence ◽  
Approximate Inverses

We investigate a new higher order iterative method for computing the generalized inverseAT,S(2)for a given matrixA. We also discuss how the new method could be applied for finding approximate inverses of nonsingular square matrices. Analysis of convergence is included to show that the proposed scheme has at least fifteenth-order convergence. Some tests are also presented to show the superiority of the new method.

scholarly journals Some novel Newton-type methods for solving nonlinear equations

2019 ◽  
Vol 38 (3) ◽  
pp. 111-123
Author(s):  
Morteza Bisheh-Niasar ◽  
Abbas Saadatmandi
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Basins Of Attraction ◽  
Sixth Order ◽  
New Method ◽  
Order Convergence ◽  
Cubic Convergence ◽  
Numerical Examples ◽  
Newton Iterative Method

The aim of this paper is to present a new nonstandard Newton iterative method for solving nonlinear equations. The convergence of the proposed method is proved and it is shown that the new method has cubic convergence. Furthermore, two new multi-point methods with sixth-order convergence, based on the introduced method, are presented. Also, we describe the basins of attraction for these methods. Finally, some numerical examples are given to show the performance of our methods by comparing with some other methods available in the literature

scholarly journals A Rapid Numerical Algorithm to Compute Matrix Inversion

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
F. Soleymani
Keyword(s):  
Convergence Rate ◽  
Numerical Algorithm ◽  
Matrix Inversion ◽  
Order Convergence ◽  
Initial Value ◽  
Numerical Examples ◽  
Seventh Order ◽  
Approximate Inverses

The aim of the present work is to suggest and establish a numerical algorithm based on matrix multiplications for computing approximate inverses. It is shown theoretically that the scheme possesses seventh-order convergence, and thus it rapidly converges. Some discussions on the choice of the initial value to preserve the convergence rate are given, and it is also shown in numerical examples that the proposed scheme can easily be taken into account to provide robust preconditioners.

scholarly journals A Numerical Method for Lane-Emden Equations Using Hybrid Functions and the Collocation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Changqing Yang ◽  
Jianhua Hou
Keyword(s):  
Differential Equation ◽  
Numerical Method ◽  
Collocation Method ◽  
Chebyshev Polynomials ◽  
Initial Value Problems ◽  
Algebraic Equations ◽  
Initial Value ◽  
Numerical Examples ◽  
Hybrid Functions ◽  
Block Pulse Functions

A numerical method to solve Lane-Emden equations as singular initial value problems is presented in this work. This method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The collocation method transforms the differential equation into a system of algebraic equations. It also has application in a wide area of differential equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.

scholarly journals A new method for solving interval and fuzzy quadratic equations of dual form

2021 ◽  
Vol 5 (2) ◽  
pp. 81-89
Author(s):  
Kamal Mamehrashi
Keyword(s):  
Numerical Method ◽  
Fuzzy Number ◽  
Quadratic Equation ◽  
New Method ◽  
Numerical Examples ◽  
Quadratic Equations ◽  
Dual Form ◽  
Interval Extension

In this paper, we present a numerical method for solving a quadratic interval equation in its dual form. The method is based on the generalized procedure of interval extension called” interval extended zero” method. It is shown that the solution of interval quadratic equation based on the proposed method may be naturally treated as a fuzzy number. An important advantage of the proposed method is that it substantially decreases the excess width defect. Several numerical examples are included to demonstrate the applicability and validity of the proposed method.

scholarly journals A Triangle Algorithm of Padé-Type Approximant for Two-Dimensional Fredholm Integral Equations of the Second Kind

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Meilan Sun ◽  
Chuanqing Gu
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Fredholm Integral Equation ◽  
Recursive Algorithm ◽  
High Order ◽  
Fredholm Integral Equations ◽  
Two Dimensional ◽  
Initial Value ◽  
Numerical Examples ◽  
Type Approximation

The function-valued Padé-type approximation (2DFPTA) is used to solve two-dimensional Fredholm integral equation of the second kind. In order to compute 2DFPTA, a triangle recursive algorithm based on Sylvester identity is proposed. The advantage of this algorithm is that, in the process of calculating 2DFPTA to avoid the calculation of the determinant, it can start from the initial value, from low to high order, and gradually proceeds. Compared with the original two methods, the numerical examples show that the algorithm is effective.

scholarly journals Variations on Hermite Methods for Wave Propagation

2017 ◽  
Vol 22 (2) ◽  
pp. 303-337 ◽  
Author(s):  
Arturo Vargas ◽  
Jesse Chan ◽  
Thomas Hagstrom ◽  
Timothy Warburton
Keyword(s):  
Wave Propagation ◽  
Time Evolution ◽  
Discontinuous Galerkin ◽  
Hermite Interpolation ◽  
High Order ◽  
New Method ◽  
Order Convergence ◽  
Hyperbolic Pdes ◽  
High Order Convergence ◽  
Dg Methods

AbstractHermite methods, as introduced by Goodrich et al. in [15], combine Hermite interpolation and staggered (dual) grids to produce stable high order accurate schemes for the solution of hyperbolic PDEs. We introduce three variations of this Hermite method which do not involve time evolution on dual grids. Computational evidence is presented regarding stability, high order convergence, and dispersion/dissipation properties for each new method. Hermite methods may also be coupled to discontinuous Galerkin (DG) methods for additional geometric flexibility [4]. An example illustrates the simplification of this coupling for Hermite methods.

scholarly journals A Newton Type Iterative Method with Fourth-order Convergence

2017 ◽  
Vol 12 (1) ◽  
pp. 87-95
Author(s):  
Jivandhar Jnawali
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Fourth Order ◽  
Newton's Method ◽  
Second Order ◽  
Secant Method ◽  
Order Derivative ◽  
Single Variable ◽  
Order Convergence ◽  
Numerical Examples

The aim of this paper is to propose a fourth-order Newton type iterative method for solving nonlinear equations in a single variable. We obtained this method by combining the iterations of contra harmonic Newton’s method with secant method. The proposed method is free from second order derivative. Some numerical examples are given to illustrate the performance and to show this method’s advantage over other compared methods.Journal of the Institute of Engineering, 2016, 12 (1): 87-95

The Mixed-Restriction Solution and its Application in Augmented Reality

2013 ◽  
Vol 380-384 ◽  
pp. 1439-1443
Author(s):  
Yan Feng ◽  
Ming Hui Wang ◽  
Chun Yun Sheng
Keyword(s):  
Augmented Reality ◽  
Iterative Method ◽  
Matrix Equation ◽  
Minimum Norm ◽  
Minimum Norm Solution ◽  
Initial Value ◽  
True Solution ◽  
Numerical Examples ◽  
The Matrix

In this paper, an iterative method is proposed to obtain the mixed-restriction solutions of . By the iterative method, the solvability of the matrix equation can be determined automatically. And if the matrix equation is consistent, then, for any initial value, the sequence generated by the iterative method, converges to the true solution within finite iteration steps in the absence of round off errors. Also, for the special initial value, the minimum norm solution can be obtained. Finally, two numerical examples are presented to demonstrate the efficiency of the iterative method.

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