ISSN:
0029-5981
Keywords:
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
The monomial method is a numerical method for solving systems of algebraic equations. It is related to Newton's method, but is based on an approximation that is monomial, rather than linear, in form. It has been shown previously that the monomial method has a number of properties not shared by Newton's method that are responsible for enhanced performance. This paper demonstrates that many of the performance characteristics of the monomial method can be explained in terms of asymptotic properties of algebraic systems, and the ability of the monomial method to exploit these properties. The monomial method recasts the algebraic system to have monomial asymptotes in all directions, so that the monomial approximation becomes asymptotically exact. This explains the very rapid movement toward a solution in the first iteration from distant starting points that has been observed with the monomial method. Problem types with ‘good asymptotics’ are found to be solved very effectively by the monomial method. Several specific engineering applications with good asymptotics are identified, and suggestions are made regarding other types of engineering applications that are likely to be handled effectively by the monomial method.
Additional Material:
9 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nme.1620372211
