Displaying similar documents to “A Macsyma implementation of Zeilberger's fast algorithm.”

Solving conics over function fields

Mark van Hoeij, John Cremona (2006)

Journal de Théorie des Nombres de Bordeaux

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Let F be a field whose characteristic is not  2 and K = F ( t ) . We give a simple algorithm to find, given a , b , c ∈ K * , a nontrivial solution in  K (if it exists) to the equation a X 2 + b Y 2 + c Z 2 = 0 . The algorithm requires, in certain cases, the solution of a similar equation with coefficients in F ; hence we obtain a recursive algorithm for solving diagonal conics over ℚ ( t 1 , ⋯ , t n ) (using existing algorithms for such equations over  ℚ ) and over 𝔽 q ( t 1 , ⋯ , t n ) .

A unified approach to some strategies for the treatment of breakdown in Lanczos-type algorithms

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...

An application of the expectation-maximization algorithm to interference rejection for direct-sequence spread-spectrum signals

Quan G. Zhang, Costas N. Georghiades (1999)

Kybernetika

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For a direct-sequence spread-spectrum (DS-SS) system we pose and solve the problem of maximum-likelihood (ML) sequence estimation in the presence of narrowband interference, using the expectation-maximization (EM) algorithm. It is seen that the iterative EM algorithm obtains at each iteration an estimate of the interference which is then subtracted from the data before a new sequence estimate is produced. Both uncoded and trellis coded systems are studied, and the EM-based algorithm...