TY - GEN

T1 - Localization of roots of a polynomial not represented in canonical form

AU - Uteshev, AY

PY - 1999

Y1 - 1999

N2 - The root isolation problem for the polynomial equation not represented in the canonical form can sometimes be solved without evaluation of the coefficients of powers of the variable. We investigate the approach based on representing first the equation in the equivalent determinantal (Hankel or block Hankel) form, and employing then Hermite's root separation method. We illustrate this for the problems of eigenvalues localization, estimation of sensitivity of the roots of the parameter dependent polynomial and nonlinear optimization.

AB - The root isolation problem for the polynomial equation not represented in the canonical form can sometimes be solved without evaluation of the coefficients of powers of the variable. We investigate the approach based on representing first the equation in the equivalent determinantal (Hankel or block Hankel) form, and employing then Hermite's root separation method. We illustrate this for the problems of eigenvalues localization, estimation of sensitivity of the roots of the parameter dependent polynomial and nonlinear optimization.

M3 - статья в сборнике материалов конференции

SN - 3-540-66047-X

SP - 431

EP - 440

BT - CASC'99: COMPUTER ALGEBRA IN SCIENTIFIC COMPUTING

A2 - Ganzha, VG

A2 - Mayr, EW

A2 - Vorozhtsov, EV

PB - Springer Nature

Y2 - 31 May 1999 through 4 June 1999

ER -