2009/02/05 by Xiaolin Qin, Qin, Xiaolin, Yong Feng +5
Computer Science · #Computational Complexity (cs.CC) #FOS: Computer and information sciences #Logic, programming, and type systems #Numerical Methods and Algorithms #Polynomial and algebraic computation #Symbolic Computation (cs.SC) #cs.CC #cs.SC
paper · pdf · doi:10.48550/arxiv.0902.0828
arxiv created 2009/02/05 · openalex publication_date 2009/02/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a new algorithm for reconstructing an exact algebraic number from its approximate value using an improved parameterized integer relation construction method. Our result is consistent with the existence of error controlling on obtaining an exact rational number from its approximation. The algorithm is applicable for finding exact minimal polynomial by its approximate root. This also enables us to provide an efficient method of converting the rational approximation representation to the minimal polynomial representation, and devise a simple algorithm to factor multivariate polynomials with rational coefficients. Compared with other methods, this method has the numerical computation advantage of high efficiency. The experimental results show that the method is more efficient than identify in Maple 11 for obtaining an exact algebraic number from its approximation. In this paper, we completely implement how to obtain exact results by numerical approximate computations.