An Efficient Formula for Linear Recurrences

Fiduccia, Charles M.

doi:10.1137/0214007

Cited by 43 publications

(26 citation statements)

References 2 publications

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“…The idea of using the latter formula to efficiently compute u i is due to Fiduccia [Fid85]. This formula expresses the fact that linear recurrence sequence extension is transposed to the remainder operation (see [BLS03, Section 5] for details).…”

Section: Resultsmentioning

confidence: 99%

New recombination algorithms for bivariate polynomial factorization based on Hensel lifting

Lecerf

2010

AAECC

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Section: Resultsmentioning

confidence: 99%

New recombination algorithms for bivariate polynomial factorization based on Hensel lifting

Lecerf

2010

AAECC

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“…An alternative to the high-order lifting is to directly use Fiduccia's algorithm for linear recurring sequences [Fiduccia, 1985]. Its complexity is slightly different and we show next that it can be interesting when β = α.…”

Section: Fiduccia's Algorithm For Linear Recurring Sequencesmentioning

confidence: 93%

Sparse approaches for the exact distribution of patterns in long state sequences generated by a Markov source

Dumas

2013

Theoretical Computer Science

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International audienceWe present two novel approaches for the computation of the exact distribution of a pattern in a long sequence. Both approaches take into account the sparse structure of the problem and are two-part algorithms. The first approach relies on a partial recursion after a fast computation of the second largest eigenvalue of the transition matrix of a Markov chain embedding. The second approach uses fast Taylor expansions of an exact bivariate rational reconstruction of the distribution. We illustrate the interest of both approaches on a simple toy-example and two biological applications: the transcription factors of the Human Chromosome 5 and the PROSITE signatures of functional motifs in proteins. On these example our methods demonstrate their complementarity and their hability to extend the domain of feasibility for exact computations in pattern problems to a new level

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“…. , u p+d−1 can be deduced for O(M(d) log(p)) operations using binary powering techniques, see [16] or [3,Sect. 3.3.3].…”

Section: P-curvature: First Ordermentioning

confidence: 99%

Fast algorithms for differential equations in positive characteristic

Bostan

Schost

2009

Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation

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We address complexity issues for linear differential equations in characteristic p > 0: resolution and computation of the p-curvature. For these tasks, our main focus is on algorithms whose complexity behaves well with respect to p. We prove bounds linear in p on the degree of polynomial solutions and propose algorithms for testing the existence of polynomial solutions in sublinear timeÕ(p 1/2 ), and for determining a whole basis of the solution space in quasi-linear timeÕ(p); theÕ notation indicates that we hide logarithmic factors. We show that for equations of arbitrary order, the p-curvature can be computed in subquadratic timeÕ(p 1.79 ), and that this can be improved to O(log(p)) for first order equations and toÕ(p) for classes of second order equations.

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An Efficient Formula for Linear Recurrences

Cited by 43 publications

References 2 publications

New recombination algorithms for bivariate polynomial factorization based on Hensel lifting

New recombination algorithms for bivariate polynomial factorization based on Hensel lifting

Sparse approaches for the exact distribution of patterns in long state sequences generated by a Markov source

Fast algorithms for differential equations in positive characteristic

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