A Non‐NP‐Complete Algorithm for a Quasi‐Fixed Polynomial Problem

Yi-Chou Chen and Hang-Chin Lai

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: Let F : ℝ × ℝ → ℝ be a real‐valued polynomial function of the form F(x,y)=∑i=0s fi(x)yi, with degree of y in F(x,y)=s≥ 1, x∈ℝ . An irreducible real‐valued polynomial function p(x) and a nonnegative integer m are given to find a polynomial function y(x) ∈ ℝ[x] satisfying the following expression: F(x, y(x)) = cpm(x) for some constant c ∈ ℝ. The constant c is dependent on the solution y(x), namely, a quasi‐fixed (polynomial) solution of the polynomial‐like equation (*). In this paper, we will provide a non‐NP‐complete algorithm to solve all quasi‐fixed solutions if the equation (*) has only a finite number of quasi‐fixed solutions.

Date: 2013
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https://doi.org/10.1155/2013/893045

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:893045

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