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Fritz G. Boese
Enclosure, separation, and computation of the zeros of exponential trinomials with constant coefficients and real exponential points
Keywords: exponential trinomials, zero locations, zero enclosure, numerical zero calculation, stability chart
After having explained the underlying motivations, we study the location of the zeros of the functions T(z):=Aeaz+Bebz+Cecz of the complex variable z with complex coefficients A, B, C and real a < b < c. As normal form of T(z)=0 serves the equation e-pz/2·sinh (z/2)=P with a complex parameter P and a real p∈(-1,1). The problem of finding all solutions z of this equation is reduced to the calculation of the unique solution in a horizontal fundamental strip F := { z∈C: -π < Im(z) ≤ π }. By detailed estimations, we find tight enclosures for the zero in F. Series expansions and algorithms to find the zero z in F are propounded. A complete stability analysis for real trinomials is given. In a discussion, the problem is set into a wider perspective.
Analysis, Oldenbourg Wissenschaftsverlag
Print ISSN: 0174-4747
Volume: 27, 01/2007
Pages: 001 - 034