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Algorithms for computing sparsest shifts of polynomials in power, Chebyshev, and Pochhammer bases

Mark Giesbrecht, Erich Kaltofen, Wen-shin Lee
2003 Journal of symbolic computation  
Our algorithms can also be applied to the Pochhammer and Chebyshev bases for the polynomials, and potentially to other bases as well.  ...  We give a new class of algorithms for computing sparsest shifts of a given polynomial.  ...  Acknowledgements This material is based on work supported in part by Natural Sciences and Engineering Research Council of Canada, the Ontario Research & Development Challenge Fund, and Maplesoft (Giesbrecht  ... 
doi:10.1016/s0747-7171(03)00087-7 fatcat:nrvwxfpd3bfirii5xubb6sl2eq

Page 3636 of Mathematical Reviews Vol. , Issue 2004e [page]

2004 Mathematical Reviews  
); Lee, Wen-shin (3-WTRL-SC; Waterloo, ON) Algorithms for computing sparsest shifts of polynomials in power, Chebyshev and Pochhammer bases.  ...  Our algorithms can also be applied to the Pochhammer and Chebyshev bases for the polynomials, and po- tentially to other bases as well.  ... 

Index

2004 Journal of symbolic computation  
, 163 GIESBRECHT, M., KALTOFEN, E. and LEE, W-S., Algorithms for computing sparsest shifts of polynomials in power, Chebyshev, and Pochhammer bases, 401 GIUSTI, M. and PARDO, L.M., Preface, 287 High-order  ...  for proving q-hypergeometric identities, 293 Index to Volume 36 A calculus combining resolution and enumeration for building finite models, 49 Algorithms for computing sparsest shifts of polynomials in  ... 
doi:10.1016/s0747-7171(03)00152-4 fatcat:gnptdsf7grf75aoiujuxvve46a

Algorithms for computing the sparsest shifts of polynomials via the Berlekamp/Massey algorithm

Mark Giesbrecht, Erich Kaltofen, Wen-shin Lee
2002 Proceedings of the 2002 international symposium on Symbolic and algebraic computation - ISSAC '02  
Acknowledgements: We thank George Labahn and three anonymous referees for their comments. Note: many of the authors' publications cited below are accessible through links in their Internet homepages.  ...  We may also consider different bases, such as Chebyshev and Pochhammer bases. The determinants considered for early termination and thus for symbolic evaluation are described in [17] .  ...  For the problem of computing a sparsest shift we have S = K n , and for computing an absolutely sparsest shift we have S = K n . In either case S need not be specified on input.  ... 
doi:10.1145/780506.780519 dblp:conf/issac/GiesbrechtKL02 fatcat:stbmtl4tcbewllqivxe5mfpuj4

Early termination in sparse interpolation algorithms

Erich Kaltofen, Wen-shin Lee
2003 Journal of symbolic computation  
In addition to dense algorithms, we implement this strategy in sparse interpolation algorithms. Based on early termination, racing algorithms execute simultaneously dense and sparse algorithms.  ...  A probabilistic strategy, early termination, enables different interpolation algorithms to adapt to the degree or the number of terms in the target polynomial when neither is supplied in the input.  ...  We have run each algorithm ten times for each polynomial with different random numbers and taken the average of the number of black box probes needed. The results are listed in Table 2 .  ... 
doi:10.1016/s0747-7171(03)00088-9 fatcat:bna2bi7uzvh5nfvlbh2feg2kka

Page 2403 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
., 2004j:14066 Giesbrecht, Mark (with Kaltofen, Erich; Lee, Wen-shin) Algorithms for computing sparsest shifts of polynomials in power, Chebyshev and Pochhammer bases.  ...  (English summary) 2004e:13041 Gil, Amparo (with Segura, Javier) A combined symbolic and numerical algorithm for the computation of zeros of orthogonal polynomials and special functions.  ... 

Page 1388 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
(Andrei Kelarev) 2004k:13047 13P05 (68W30) — (with Giesbrecht, Mark; Kaltofen, Erich) Algorithms for computing sparsest shifts of polynomials in power, Chebyshev and Pochhammer bases.  ...  (English summary) Computing and combinatorics, 153-161, Lecture Notes in Comput.  ...