منابع مشابه
Zero sets of univariate polynomials
Let L be the zero set of a nonconstant monic polynomial with complex coe¢ cients. In the context of constructive mathematics without countable choice, it may not be possible to construct an element of L. In this paper we introduce a notion of distance from a point to a subset, more general than the usual one, that allows us to measure distances to subsets like L. To verify the correctness of th...
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Polynomials with perturbed coefficients, which can be regarded as interval polynomials, are very common in the area of scientific computing due to floating point operations in a computer environment. In this paper, the zeros of interval polynomials are investigated. We show that, for a degree n interval polynomial, the number of interval zeros is at most n and the number of complex block zeros ...
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The zero sets of harmonic polynomials play a crucial role in the study of the free boundary regularity problem for harmonic measure. In order to understand the fine structure of these free boundaries a detailed study of the singular points of these zero sets is required. In this paper we study how “degree k points” sit inside zero sets of harmonic polynomials in R of degree d (for all n ≥ 2 and...
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− The problem of finding the greatest common divisor (GCD) of univariate polynomials appears in many engineering fields. Despite its formulation is well-known, it is an ill-posed problem that entails numerous difficulties when the coefficients of the polynomials are not known with total accuracy, as, for example, when they come from measurement data. In this work we propose a novel GCD estimati...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2010
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-2010-05086-x