ISSN:
1436-4646
Keywords:
Roots of Polynomials
;
Fixed Point Computing Methods
;
Complementary Pivoting Methods
;
Piecewise Linear Homotopy
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract This paper presents a constructive method which gives, for any polynomialF(Z) of the degreen, approximate values of all the roots ofF(Z).. The point of the method is on the use of a piecewise linear function $$\bar H$$ (Z, t) which approximates a homotopyH(Z, t) betweenF(Z) and a polynomialG(Z) of the degreen withn known simple roots. It is shown that the set of solutions to $$\bar H$$ (Z, t) = 0 includesn distinct paths,m of which converges to a root ofF(Z) if and only if the root has the multiplicitym. Starting from givenn roots ofG(Z), a complementary pivot algorithm generates thosen paths.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01582093
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