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Shor's algorithm is a quantum algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor...

time needed for a multiplication, whichever multiplication algorithm is used. Discussion will refer to the form N / D = ( Q , R ) {\displaystyle N/D=(Q...

equivalent to a one-state Markov decision process. The regret ρ {\displaystyle \rho } after T {\displaystyle T} rounds is defined as the expected difference...

Index calculus algorithm Number field sieve Pohlig–Hellman algorithm Pollard's rho algorithm for logarithms Pollard's kangaroo algorithm (aka Pollard's...

The Schönhage–Strassen algorithm is an asymptotically fast multiplication algorithm for large integers, published by Arnold Schönhage and Volker Strassen...

y {\displaystyle y} and k {\displaystyle k} be non-negative integers. Algorithms that compute (the decimal representation of) y {\displaystyle {\sqrt {y}}}...

practice because their highly structured geometry is well-suited for algorithmic detection and processing. The appearance of chessboards in computer vision...

primality test and cyclotomic AKS test) is a deterministic primality-proving algorithm created and published by Manindra Agrawal, Neeraj Kayal, and Nitin Saxena...

the general number field sieve (GNFS) is the most efficient classical algorithm known for factoring integers larger than 10100. Heuristically, its complexity...

{\displaystyle \rho _{0}} , so that the state at any later time is given by ρ ( t ) = e L t [ ρ 0 ] {\displaystyle \rho (t)=e^{Lt}[\rho _{0}]} . Then the...

{\partial \rho }{\partial t}}+(\nabla \rho )\cdot \mathbf {u} +\rho (\nabla \cdot \mathbf {u} )={\frac {\partial \rho }{\partial t}}+\nabla \cdot (\rho \mathbf...

is: F d = 1 2 ρ u 2 c d A {\displaystyle F_{\rm {d}}\,=\,{\tfrac {1}{2}}\,\rho \,u^{2}\,c_{\rm {d}}\,A} where F d {\displaystyle F_{\rm {d}}} is the drag...

{1}{\rho }}{\frac {dP}{dx}}\\[1ex]\rightarrow dP&=(-\rho \,dv){\frac {dx}{dt}}=(v\,d\rho )v\\[1ex]\rightarrow v^{2}&\equiv c^{2}={\frac {dP}{d\rho }}\end{aligned}}}...

traditional quadratic optimization methods, including the Critical Line Algorithm (CLA) of Markowitz. HRP addresses three central issues commonly associated...

(-\nabla \phi )=-4\pi G\rho ,} yields Poisson's equation for gravity: ∇ 2 ϕ = 4 π G ρ . {\displaystyle \nabla ^{2}\phi =4\pi G\rho .} If the mass density...

{\displaystyle n={\frac {4R\rho }{(R+\rho )^{2}}}} , m = 4 R ρ ( R + ρ ) 2 + ζ 2 {\displaystyle m={\frac {4R\rho }{(R+\rho )^{2}+\zeta ^{2}}}} , K ( m...

ρ ) = S ( ρ 1 ) + S ( ρ 2 ) . {\displaystyle S(\rho )=S(\rho _{1})+S(\rho _{2}).} The above discussion generalizes easily to the case of a quantum system...

particles. In an algorithm, there are collision and streaming steps. These evolve the density of the fluid ρ ( x → , t ) {\displaystyle \rho ({\vec {x}},t)}...

In statistics, Markov chain Monte Carlo (MCMC) is a class of algorithms used to draw samples from a probability distribution. Given a probability distribution...

statistics, Alternating Conditional Expectations (ACE) is a nonparametric algorithm used in regression analysis to find the optimal transformations for both...