Enclosure, separation, and computation of the zeros of exponential trinomials with constant coefficients and real exponential points
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Fritz G. Boese
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.
© Oldenbourg Wissenschaftsverlag
Articles in the same Issue
- Enclosure, separation, and computation of the zeros of exponential trinomials with constant coefficients and real exponential points
- Asymptotic estimates for a semigroup related to compressible viscous fluid flow
- Oscillation of first order neutral differential equations of Euler form
- WENO-TVD schemes for hyperbolic conservation laws
- Special functions and the Mellin transforms of Laguerre and Hermite functions
- On a class of extremal solutions of the nondegenerate matricial Carathéodory problem
- Removable singularities of fully nonlinear elliptic equations
Articles in the same Issue
- Enclosure, separation, and computation of the zeros of exponential trinomials with constant coefficients and real exponential points
- Asymptotic estimates for a semigroup related to compressible viscous fluid flow
- Oscillation of first order neutral differential equations of Euler form
- WENO-TVD schemes for hyperbolic conservation laws
- Special functions and the Mellin transforms of Laguerre and Hermite functions
- On a class of extremal solutions of the nondegenerate matricial Carathéodory problem
- Removable singularities of fully nonlinear elliptic equations
