Displaying similar documents to “Algorithm 4. Polynomial decomposition into quadratic factors with controlled accuracy by Bairstow's method”

Branch-delete-bound algorithm for globally solving quadratically constrained quadratic programs

Zhisong Hou, Hongwei Jiao, Lei Cai, Chunyang Bai (2017)

Open Mathematics

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This paper presents a branch-delete-bound algorithm for effectively solving the global minimum of quadratically constrained quadratic programs problem, which may be nonconvex. By utilizing the characteristics of quadratic function, we construct a new linearizing method, so that the quadratically constrained quadratic programs problem can be converted into a linear relaxed programs problem. Moreover, the established linear relaxed programs problem is embedded within a branch-and-bound...

Improvements on the Cantor-Zassenhaus factorization algorithm

Michele Elia, Davide Schipani (2015)

Mathematica Bohemica

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The paper presents a careful analysis of the Cantor-Zassenhaus polynomial factorization algorithm, thus obtaining tight bounds on the performances, and proposing useful improvements. In particular, a new simplified version of this algorithm is described, which entails a lower computational cost. The key point is to use linear test polynomials, which not only reduce the computational burden, but can also provide good estimates and deterministic bounds of the number of operations needed...

Nonmonotone strategy for minimization of quadratics with simple constraints

M. A. Diniz-Ehrhardt, Zdeněk Dostál, M. A. Gomes-Ruggiero, J. M. Martínez, Sandra Augusta Santos (2001)

Applications of Mathematics

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An algorithm for quadratic minimization with simple bounds is introduced, combining, as many well-known methods do, active set strategies and projection steps. The novelty is that here the criterion for acceptance of a projected trial point is weaker than the usual ones, which are based on monotone decrease of the objective function. It is proved that convergence follows as in the monotone case. Numerical experiments with bound-constrained quadratic problems from CUTE collection show...

A polynomial reduction algorithm

Henri Cohen, Francisco Diaz Y Diaz (1991)

Journal de théorie des nombres de Bordeaux

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The algorithm described in this paper is a practical approach to the problem of giving, for each number field K a polynomial, as canonical as possible, a root of which is a primitive element of the extension K / ℚ . Our algorithm uses the L L L algorithm to find a basis of minimal vectors for the lattice of ℝ n determined by the integers of K under the canonical map.