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Odlyzko–Schönhage Algorithm
In mathematics, the Odlyzko–Schönhage algorithm is a fast algorithm for evaluating the Riemann zeta function at many points, introduced by . The main point is the use of the fast Fourier transform to speed up the evaluation of a finite Dirichlet series of length ''N'' at O(''N'') equally spaced values from O(''N''2) to O(''N''1+ε) steps (at the cost of storing O(''N''1+ε) intermediate values). The Riemann–Siegel formula used for calculating the Riemann zeta function with imaginary part ''T'' uses a finite Dirichlet series with about ''N'' = ''T''1/2 terms, so when finding about ''N'' values of the Riemann zeta function it is sped up by a factor of about ''T''1/2. This reduces the time to find the zeros of the zeta function with imaginary part at most ''T'' from about ''T''3/2+ε steps to about ''T''1+ε steps. The algorithm can be used not just for the Riemann zeta function, but also for many other functions given by Dirichlet series. The algorithm was used by to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use Conditional (computer programming), conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning). In contrast, a Heuristic (computer science), heuristic is an approach to solving problems without well-defined correct or optimal results.David A. Grossman, Ophir Frieder, ''Information Retrieval: Algorithms and Heuristics'', 2nd edition, 2004, For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation. As an e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
