ISSN:
0029-5981
Keywords:
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
The monomial method solves systems of non-linear algebraic equations by constructing a sequence of approximating monomial (single-term polynomial) systems, much as Newton's method generates a sequence of linear systems to do this. Since the monomial system becomes linear through a logarithmic transformation of variables, the monomial method can be considered to be an alternative linearization scheme. Although the monomial method is closely related to Newton's method, it exhibits many special invariance properties not shared by Newton's method that enhance performance. This paper first briefly reviews the monomial method and its special properties. Two new versions of the algorithm are presented, both of which, are simplified and computationally more efficient to implement in comparison to the original algorithm. The monomial method is also extended to apply to certain non-algebraic systems. Since the monomial method can be interpreted as Newton's method applied to a three-part reformulation of the algebraic system, graphical experiments are presented which investigate the role that each part of the reformulation plays in contributing to the enchanced performance. Finally, instances in which difficulties have arisen using the monomial method are discussed.
Additional Material:
3 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nme.1620371206
