Details:
| Title | On Solving Composite Power Polynomial Equations | | Author(s) | Christoforos N. Hadjicostis, Yingquan Wu | | Type | Technical Report, Misc | | Abstract | It is well known that a system of power polynomial equations can be reduced to a single-variable polynomial equation by exploiting the so-called Newton's identities. In this work, by further exploring Newton's identities, we discover a binomial decomposition rule for composite elementary symmetric polynomials. Utilizing this decomposition rule, we solve three types of systems of composite power polynomial equations by converting each type to single-variable polynomial equations that can be solved easily. For each type of system, we discuss potential applications, and characterize the number of non-trivial solutions (up to permutations) and the complexity of our proposed algorithmic procedure.
| | Keywords | Power polynomial, composite power polynomial, Newton's
identities, system
of polynomial equations
|
| Language | English | | Year | 2005 | | Edition | 0 | | Translation |
No | | Refereed |
No |
|
