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Polynomial Real Root Isolation Using Descarte's Rule of Signs * George E. Collins
 

Summary: Polynomial Real Root Isolation Using Descarte's Rule of Signs *
George E. Collins
and
Alkiviadis G. Akritas
Computer Sciences Department, University of Wisconsin
1210 W. Dayton Street, Madison, Wisconsin 53706
Abstract
Uspensky's 1948 book on the theory of equations
presents an algorithm, based on Descartes' rule
of signs, for isolating the real roots of a
squarefree polynomial with real coefficients.
Programmed in SAC-I and applied to several classes
of polynomials with integer coefficients,
Uspensky's method proves to be a strong competitor
of the recently discovered algorithm of Collins and
Loos. It is shown, however, that it's maximum
computing time is exponential in the coefficient
length. This motivates a modification of the
Uspensky algorithm which is quadratic in the
coefficient length and which also performs well in

  

Source: Akritas, Alkiviadis G. - Department of Computer and Communication Engineering, University of Thessaly

 

Collections: Computer Technologies and Information Sciences