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When are Two Numerical Polynomials Relatively Prime?

โœ Scribed by B. Beckermann; G. Labahn

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
426 KB
Volume
26
Category
Article
ISSN
0747-7171

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โœฆ Synopsis

Let a and b be two polynomials having numerical coefficients. We consider the question: When are a and b relatively prime? Since the coefficients of a and b are approximant, the question is the same as: When are two polynomials relatively prime, even after small perturbations of the coefficients?

In this paper we provide a numeric parameter for determining whether two polynomials are prime, even under small perturbations of the coefficients. Our methods rely on an inversion formula for Sylvester matrices to establish an effective criterion for relative primeness. The inversion formula can also be used to approximate the condition number of a Sylvester matrix.

๐Ÿ“œ SIMILAR VOLUMES

A Fast and Numerically Stable Euclidean-
A Fast and Numerically Stable Euclidean-like Algorithm for Detecting Relatively Prime Numerical Polynomials
โœ B. Beckermann; G. Labahn ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 644 KB

In this paper we provide a fast, numerically stable algorithm to determine when two given polynomials a and b are relatively prime and remain relatively prime even after small perturbations of their coefficients. Such a problem is important in many applications where input data are only available up