### Algorithm 7. Evaluation of a trigonometric polynomial

Lucja Sobich (1970)

Applicationes Mathematicae

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Lucja Sobich (1970)

Applicationes Mathematicae

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Anna Bartkowiak (1974)

Applicationes Mathematicae

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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 $K/\mathbb{Q}$. Our algorithm uses the $LLL$ algorithm to find a basis of minimal vectors for the lattice of ${\mathbb{R}}^{n}$ determined by the integers of $K$ under the canonical map.

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...

A. El Guennouni (1999)

Applicationes Mathematicae

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The Lanczos method for solving systems of linear equations is implemented by using some recurrence relationships between polynomials of a family of formal orthogonal polynomials or between those of two adjacent families of formal orthogonal polynomials. A division by zero can occur in these relations, thus producing a breakdown in the algorithm which has to be stopped. In this paper, three strategies to avoid this drawback are discussed: the MRZ and its variants, the normalized and unnormalized...

Kotsios, Stelios (2007)

Applied Mathematics E-Notes [electronic only]

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Carothers, David C., Parker, G.Edgar, Sochacki, James S., Warne, Paul G. (2005)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Lai, Jiangzhou, Lu, Linzhang, Xu, Shiji (2011)

Mathematical Problems in Engineering

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Di Biase, Fausto, Urbanke, Rüdiger (1995)

Experimental Mathematics

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Caruso, Fabrizio (1999)

Séminaire Lotharingien de Combinatoire [electronic only]

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