Towards More Accurate Separation Bounds of Empirical Polynomials II
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We study the problem of bounding a polynomial which is absolutely irreducible, away from polynomials which are not absolutely irreducible. These separation bounds are useful for testing whether an empirical polynomial is absolutely irreducible or not, for the given tolerance or error bound of its coefficients. In the former paper, we studied some improvements on Kaltofen and May’s method which finds applicable separation bounds using an absolute irreducibility criterion due to Ruppert. In this paper, we study the similar improvements on the method using the criterion due to Gao and Rodrigues for sparse polynomials satisfying Newton polytope conditions, by which we are able to find more accurate separation bounds, for such bivariate polynomials. We also discuss a concept of separation bound continuations for both dense and sparse polynomials.
KeywordsFrobenius Norm Block Matrice Separation Bound Index Pair Bivariate Polynomial
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