Details:
Title  The BMS algorithm.  Author(s)  Shojiro Sakata  Type  Book, Chapter in Book, Conference Proceeding  Abstract  We present a sketch of the ndimensional (nD) Berlekamp–Massey algorithm (alias Berlekamp–Massey–Sakata or BMS algorithm) w.r.t. nD arrays. That is: (1) How is it related to Gröbner basis? (2) What problem can it solve? (3) How does it work? (4) Its variations. First we discuss another problem closely related to our main problem, and introduce some concepts about nD linear recurrences and modules of nD arrays as their general solutions. These two problems are just the inverse (or rather dual) to each other, which can be solved by the Buchberger algorithm (Buchberger in Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal, Ph.D. thesis, Innsbruck, 1965; J. Symb. Comput. 41(3–4):475–511, 2006; Multidimensional systems theory, Reidel, Dordrecht, pp. 184–232, 1985; Mora in Gröbner technology, this volume, pp. 11–25, 2009b), and the BMS algorithm, respectively. Furthermore, we discuss some properties of BMS algorithm and its outputs, including its computational complexity, as well as several variations of the BMS algorithm.  ISBN  9783540938057/hbk; 97835 
URL 
http://link.springer.com/chapter/10.1007%2F9783540938064_9 
Language  English  Pages  143163  Publisher  Berlin: Springer  Year  2009  Edition  0  Translation 
No  Refereed 
No 
