Abstract
 [*] Stability radius of polynomials occurring in the numerical
solution of initial value problems
 van der Marel R.P.
 BIT, 30, 516528, 1990
 © 1990. BIT. All Rights Reserved.

This paper deals with polynomial approximations phi(x) to the
exponential function exp(x) related to numerical procedures for
solving initial value problems. Motivated by stability requirements,
we present a numerical study of the largest disk D(rho) = {z in C:
z+rho <= rho} that is contained in the stability region S(phi) = {z
in C: phi(z) <= 1}. The radius of this largest disk is denoted by
r(phi), the stability radius. On the basis of our numerical study,
several conjectures are made concerning r_{m,p} = sup{r(phi): phi in
Pi_{m,p}}. Here Pi_{m,p} (1 <= p <= m; p,m integers) is the
class of all polynomials phi(x) with real coefficients and degree
<= m for which phi(x) = exp(x) + O(x^{p+1}) (for x > 0).
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Last modified December 8, 1998.
Roeland van der Marel,
marel@stsci.edu.
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