An Analysis of Polynomial Composition
نویسنده
چکیده
An analysis is made of the runtime of a previously published algorithm for polynomial composition. Two new, more eecient algorithms are presented. One of these algorithms is optimal, while the other algorithm is numerically more stable than the optimal one. Additionally, as a generalization of polynomial composition, we show how to compose a multiaane function with a set of polynomials as an extension to an earlier algorithm for composing two polynomial functions. With this extension, we are able to perform degree raising with composition.
منابع مشابه
Some new families of definite polynomials and the composition conjectures
The planar polynomial vector fields with a center at the origin can be written as an scalar differential equation, for example Abel equation. If the coefficients of an Abel equation satisfy the composition condition, then the Abel equation has a center at the origin. Also the composition condition is sufficient for vanishing the first order moments of the coefficients. The composition conjectur...
متن کاملSome New Results On the Hosoya Polynomial of Graph Operations
The Wiener index is a graph invariant that has found extensive application in chemistry. In addition to that a generating function, which was called the Wiener polynomial, who’s derivate is a q-analog of the Wiener index was defined. In an article, Sagan, Yeh and Zhang in [The Wiener Polynomial of a graph, Int. J. Quantun Chem., 60 (1996), 959969] attained what graph operations do to the Wiene...
متن کاملNarumi-Katayama Polynomial of Some Nano Structures
The Narumi-Katayama index is the first topological index defined by the product of some graph theoretical quantities. Let G be a simple graph. Narumi-Katayama index of G is defined as the product of the degrees of the vertices of G. In this paper, we define the Narumi-Katayama polynomial of G. Next, we investigate some properties of this polynomial for graphs and then, we obtain ...
متن کاملAn efficient symmetric polynomial-based key establishment protocol for wireless sensor networks
An essential requirement for providing secure services in wireless sensor networks is the ability to establish pairwise keys among sensors. Due to resource constraints on the sensors, the key establishment scheme should not create significant overhead. To date, several key establishment schemes have been proposed. Some of these have appropriate connectivity and resistance against key exposure, ...
متن کاملL$^q$ inequalities for the ${s^{th}}$ derivative of a polynomial
Let $f(z)$ be an analytic function on the unit disk ${zinmathbb{C}, |z|leq 1}$, for each $q>0$, the $|f|_{q}$ is defined as followsbegin{align*}begin{split}&left|fright|_q:=left{frac{1}{2pi}int_0^{2pi}left|f(e^{itheta})right|^qdthetaright}^{1/q}, 0
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1995