Higher-order iteration functions for simultaneously approximating polynomial zeros

1983 ◽  
Vol 14 (1) ◽  
pp. 45-58 ◽  
Author(s):  
G. Loizou
Keyword(s):  
Higher Order ◽  
Polynomial Zeros ◽  
Iteration Functions

New higher-order methods for the simultaneous inclusion of polynomial zeros

2011 ◽  
Vol 58 (2) ◽  
pp. 179-201 ◽  
Author(s):  
Miodrag S. Petković ◽  
Mimica R. Milošević ◽  
Dušan M. Milošević
Keyword(s):  
Higher Order ◽  
Polynomial Zeros ◽  
Higher Order Methods

Some higher-order iteration functions for solving nonlinear models

2018 ◽  
Vol 334 ◽  
pp. 80-93 ◽  
Author(s):  
Abdullah Khamis Hassan Alzahrani ◽  
Ramandeep Behl ◽  
Ali Saleh Alshomrani
Keyword(s):  
Nonlinear Models ◽  
Higher Order ◽  
Iteration Functions

scholarly journals Two Classes of Iteration Functions and Q-Convergence of Two Iterative Methods for Polynomial Zeros

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 371
Author(s):  
Petko D. Proinov
Keyword(s):  
Fixed Point ◽  
Iterative Methods ◽  
Local Convergence ◽  
Initial Approximation ◽  
Vector Spaces ◽  
Polynomial Zeros ◽  
High Q ◽  
Iteration Functions ◽  
Iteration Function ◽  
Local Convergence Analysis

In this work, two broad classes of iteration functions in n-dimensional vector spaces are introduced. They are called iteration functions of the first and second kind at a fixed point of the corresponding iteration function. Two general local convergence theorems are presented for Picard-type iterative methods with high Q-order of convergence. In particular, it is shown that if an iterative method is generated by an iteration function of first or second kind, then it is Q-convergent under each initial approximation that is sufficiently close to the fixed point. As an application, a detailed local convergence analysis of two fourth-order iterative methods is provided for finding all zeros of a polynomial simultaneously. The new results improve the previous ones for these methods in several directions.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

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