Power Series Composition and Change of Basis

@misc{citeulike:2678849, abstract = {Efficient algorithms are known for many operations on truncated power series (multiplication, powering, exponential, ...). Composition is a more complex task. We isolate a large class of power series for which composition can be performed efficiently. We deduce fast algorithms for converting polynomials between various bases, including Euler, Bernoulli, Fibonacci, and the orthogonal Laguerre, Hermite, Jacobi, Krawtchouk, Meixner and Meixner-Pollaczek.}, author = {Bostan, Alin and Salvy, Bruno and Schost, \&\#xc9;ric }, citeulike-article-id = {2678849}, eprint = {0804.2337}, keywords = {algorithms, computation, mathematics}, month = {Apr}, posted-at = {2008-04-16 20:58:25}, priority = {2}, title = {Power Series Composition and Change of Basis}, url = {http://arxiv.org/abs/0804.2337}, year = {2008} }

TY - ELEC ID - citeulike:2678849 L3 - citeulike-article-id:2678849 TI - Power Series Composition and Change of Basis N2 - Efficient algorithms are known for many operations on truncated power series (multiplication, powering, exponential, ...). Composition is a more complex task. We isolate a large class of power series for which composition can be performed efficiently. We deduce fast algorithms for converting polynomials between various bases, including Euler, Bernoulli, Fibonacci, and the orthogonal Laguerre, Hermite, Jacobi, Krawtchouk, Meixner and Meixner-Pollaczek. KW - algorithms KW - computation KW - mathematics AU - Bostan, Alin AU - Salvy, Bruno AU - Schost, Éric PY - 2008/Apr/15/ UR - http://arxiv.org/abs/0804.2337 ER -