1983 | OriginalPaper | Buchkapitel
Real Zeros of Polynomials
verfasst von : Prof. Dr. G. E. Collins, Prof. Dr. R. Loos
Erschienen in: Computer Algebra
Verlag: Springer Vienna
Enthalten in: Professional Book Archive
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Let A be a polynomial over Z, Q or Q(α) where α is a real algebraic number. The problem is to compute a sequence of disjoint intervals with rational endpoints, each containing exactly one real zero of A and together containing all real zeros of A. We describe an algorithm due to Kronecker based on the minimum root Separation, Sturm’s algorithm, an algorithm based on Rolle’s theorem due to Collins and Loos and the modified Uspensky algorithm due to Collins and Aritas. For the last algorithm a recursive version with correctness proof is given which appears in print for the first time.