Faster algorithms for the characteristic polynomial

A new randomized algorithm is presented for computing the characteristic polynomial of an n × n matrix over a field. Over a sufficiently large field the asymptotic expected complexity of the algorithm is O(nθ ) field operations, improving by a factor of log n on the worst case complexity of Keller– Gehrig’s algorithm [11]. Categories and Subject Descriptors: F.2 [Theory of computation]: Analysis of algorithms and problem Complexity; I.1 [Computing Methodology]: Symbolic and algebraic manipulation: Algorithms General Terms: Algorithms

• Type: Conference
• Year: 2007
• Where: ISSAC
• Authors: Clément Pernet, Arne Storjohann
• Keywords: Algorithms, Asymptotic Expected Complexity, ISSAC 2007, Worst Case Complexity