β Scribed by G. Malajovich; J.P. Zubelli
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This paper concerns the fast numerical factorization of degree a + b polynomials in a neighborhood of the polynomial x a. We want to obtain the so-called splitting of one such polynomial, i.e., a degree a factor with roots close to zero and a degree b factor with roots close to infinity. An important application of splitting is complete polynomial factorization or root finding.
A new algorithm for splitting polynomials is presented. This algorithm requires O(d log e -1)1+6 floating point operations, with O(log e-l) 1+~ bits of precision. As far as complexity is concerned, this is the fastest algorithm known by the authors for that problem.
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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
We discuss efficient conversion algorithms for orthogonal polynomials. We describe a known conversion algorithm from an arbitrary orthogonal basis to the monomial basis, and deduce a new algorithm of the same complexity for the converse operation.