Details:
Title  Guessing singular dependencies  Author(s)  Joris van der Hoeven  Type  Article in Journal  Abstract  Abstract Given d complex numbers z_1 , … , z_d , it is classical that linear dependencies λ_1 z_1 + ⋯ + λ_d z_d = 0 with λ_1 , … , λ_d ∈ Z can be guessed using the LLLalgorithm. Similarly, given d formal power series f_1 , … , f_d ∈ C [ [ z ] ] , algorithms for computing Padé–Hermite forms provide a way to guess relations P_1 f_1 + ⋯ + P_d f_d = 0 with P_1 , … , P_d ∈ C [ z ] . Assuming that f_1 , … , f_d have a radius of convergence r > 0 and given a real number R > r , we will describe a new algorithm for guessing linear dependencies of the form g_1 f_1 + ⋯ + g_d f_d = h , where g_1 , … , g_d , h ∈ C [ [ z ] ] have a radius of convergence ≥R. We will also present two alternative algorithms for the special cases of algebraic and Fuchsian dependencies.  Keywords  Guessing, Asymptotic dependency, Orthogonalization, Analytic continuation, Fuchsian singularity, Padé–Hermite forms, Algorithm  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717113000977 
Language  English  Journal  Journal of Symbolic Computation  Volume  59  Number  0  Pages  54  80  Year  2013  Edition  0  Translation 
No  Refereed 
No 
