scholarly journals On the observed rate of convergence of an iterative method applied to a model elliptic difference equation

1978 ◽  
Vol 32 (141) ◽  
pp. 127-127 ◽  
Author(s):  
R. A. Nicolaides
Keyword(s):  
Difference Equation ◽  
Iterative Method ◽  
Rate Of Convergence ◽  
Elliptic Difference ◽  
Elliptic Difference Equation

scholarly journals Geometry of an elliptic difference equation related to Q4

2016 ◽  
Vol 93 (3) ◽  
pp. 763-784 ◽  
Author(s):  
James Atkinson ◽  
Phil Howes ◽  
Nalini Joshi ◽  
Nobutaka Nakazono
Keyword(s):  
Difference Equation ◽  
Elliptic Difference ◽  
Elliptic Difference Equation

scholarly journals On the Rate of Convergence of P-Iteration, SP-Iteration, and D-Iteration Methods for Continuous Nondecreasing Functions on Closed Intervals

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Jukkrit Daengsaen ◽  
Anchalee Khemphet
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Rate Of Convergence ◽  
Convergence Theorem ◽  
Computational Cost ◽  
Closed Intervals ◽  
Iteration Methods ◽  
Nondecreasing Functions ◽  
New Iterative Method

We introduce a new iterative method called D-iteration to approximate a fixed point of continuous nondecreasing functions on arbitrary closed intervals. The purpose is to improve the rate of convergence compared to previous work. Specifically, our main result shows that D-iteration converges faster than P-iteration and SP-iteration to the fixed point. Consequently, we have that D-iteration converges faster than the others under the same computational cost. Moreover, the analogue of their convergence theorem holds for D-iteration.

scholarly journals A Seventh-Order Scheme for Computing the Generalized Drazin Inverse

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 622 ◽  
Author(s):  
Dilan Ahmed ◽  
Mudhafar Hama ◽  
Karwan Hama Faraj Jwamer ◽  
Stanford Shateyi
Keyword(s):  
Iterative Method ◽  
Rate Of Convergence ◽  
Generalized Inverses ◽  
Drazin Inverse ◽  
Computational Tool ◽  
Initial Matrix ◽  
Matrix Products ◽  
Seventh Order ◽  
Order Scheme ◽  
Generalized Drazin Inverse

One of the most important generalized inverses is the Drazin inverse, which is defined for square matrices having an index. The objective of this work is to investigate and present a computational tool in the form of an iterative method for computing this task. This scheme reaches the seventh rate of convergence as long as a suitable initial matrix is chosen and by employing only five matrix products per cycle. After some analytical discussions, several tests are provided to show the efficiency of the presented formulation.

scholarly journals On a Cubically Convergent Iterative Method for Matrix Sign

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
M. Sharifi ◽  
S. Karimi Vanani ◽  
F. Khaksar Haghani ◽  
M. Arab ◽  
S. Shateyi
Keyword(s):  
Iterative Method ◽  
Rate Of Convergence ◽  
Global Behavior ◽  
Matrix Sign Function ◽  
Sign Function

We propose an iterative method for finding matrix sign function. It is shown that the scheme has global behavior with cubical rate of convergence. Examples are included to show the applicability and efficiency of the proposed scheme and its reciprocal.

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