Peter Kirrinnis

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The subject of this paper is fast numerical algorithms for factoring univariate polynomials with complex coefficients and for computing partial fraction decom-positions (PFDs) of rational functions in C(z). Numerically stable and computa-tionally feasible versions of PFD are specified first for the special case of rational functions with all singularities(More)
In this paper the problem of computing the numerical value of the integral (P q(z)/p(z)dz, where q and p are polynomials, .-. given by their coefficients, and 17is a curve in the complex plane, is investigated from the point of view of (serial) bit coraplezity, i.e., finite precision arithmetic is used. The first algorithm presented computes this integral(More)
Factors of polynomials with complex coeecients can be computed eeciently by m ultidimensional Newton iteration, applied to the coeecient vectors. We describe and analyze eecient numerical algorithms for factorization and partial fraction decomposition which are based on this classical approach. The convergence proof provides algorithmically useful starting(More)
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