Nondiagonal quadratic Hennite-Pade approximation to the exponential function
[摘要] Approximation to the exponential function of the form E(mns)(z):=P-n(z)e(-2z)+Q(m)(z)e(-z)+R(s)(z)=O(z(m+n+s+2)), where P-n, Q(m), and R(s) are polynomials of degree at most n,m and s, respectively, and P-n has leading coefficient 1 is considered. Explicit formulas for the polynomials P-n, Q(m) and R(s) are obtained by using some identities involving hypergeometric series in the case of R,. An exact asymptotic expression as m + n --> infinity is obtained for the error function Em(ns) and it is also shown that these Hermite-Pade Type I polynomials can be used to asymptotically minimize expressions of the above form on the unit disk.
[发布日期] 1995-12-29 [发布机构]
[效力级别] Proceedings Paper [学科分类]
[关键词] Hermite-Pade approximant;exponential function;Hermite-Pade type I polynomials;hypergeometric series;error asymptotics [时效性]
