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[*] Stability radius of polynomials occurring in the numerical solution of initial value problems
van der Marel R.P.
BIT, 30, 516-528, 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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