scholarly journals XI. Analysis of the roots of equations

1837 ◽  
Vol 127 ◽  
pp. 161-178
Keyword(s):  
Roots Of Unity ◽  
Constituent Part ◽  
Roots Of Equations

1. The object of this memoir is to show how the constituent parts of the roots of algebraical equations may be determined, by considering the conditions under which they vanish, and conversely to show the signification of each such constituent part. 2. In equations of degrees higher than the second the same constituent part of the root is found in several places governed by the same radical sign, but affected with the different corresponding roots of unity as multipliers.

scholarly journals On Stability of Iterative Sequences with Error

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 765 ◽  
Author(s):  
Abed ◽  
Taresh
Keyword(s):  
Fixed Point ◽  
Unique Fixed Point ◽  
Contractive Mapping ◽  
Systems Of Equations ◽  
Operator Equations ◽  
Mann Iteration ◽  
Accretive Mappings ◽  
Non Linear Systems ◽  
Roots Of Equations ◽  
Linear Systems Of Equations

Iterative methods were employed to obtain solutions of linear and non-linear systems of equations, solutions of differential equations, and roots of equations. In this paper, it was proved that s-iteration with error and Picard–Mann iteration with error converge strongly to the unique fixed point of Lipschitzian strongly pseudo-contractive mapping. This convergence was almost F-stable and F-stable. Applications of these results have been given to the operator equations Fx=f and x+Fx=f, where F is a strongly accretive and accretive mappings of X into itself.

scholarly journals IV. A general method for exhibiting the value of an algebraic expression involving several radical quantities in an infinite series: wherein Sir Isaac Newton’s theorem for involving a binomial, with another of the same author, relating to the roots of equations, are demonstrated

1752 ◽  
Vol 47 ◽  
pp. 20-27 ◽  
Keyword(s):  
Infinite Series ◽  
Algebraic Expression ◽  
Roots Of Equations ◽  
General Method

Among all the great improvements, which the art of computation hath in these last ages received, the most considerable; since not only the doctrine of chances and annuites, with some other branches of the mathematics, depend almost intirely thereon, but even the business of fluents, of such extensive use, would, without its aid and concurrence, be quite at a stand in a multitude of cases, as is well known to mathematicians.

On the Roots of Equations

The Analyst ◽  
1878 ◽  
Vol 5 (2) ◽  
pp. 51 ◽  
Author(s):  
Professor Worpitzky
Keyword(s):  
Roots Of Equations
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