RSA Cryptography: Factorization
... sage: timeit(’factor(n)’) 5 loops, best of 3: 160 ms per loop From this we can see that not all numbers of a given length take the same amount of time to factor. For example a 100 digit number took just 160 milliseconds to factor while a 65 digit number took 20.3 seconds. This suggests that certain ...
... sage: timeit(’factor(n)’) 5 loops, best of 3: 160 ms per loop From this we can see that not all numbers of a given length take the same amount of time to factor. For example a 100 digit number took just 160 milliseconds to factor while a 65 digit number took 20.3 seconds. This suggests that certain ...
ASB Presentation - The University of Sheffield
... • In this paper, a decomposition based evolutionary algorithm with adaptive epsilon comparison is introduced to solve unconstrained and constrained many objective optimization problems. • The approach utilizes reference directions to guide the search, wherein the reference directions are generated u ...
... • In this paper, a decomposition based evolutionary algorithm with adaptive epsilon comparison is introduced to solve unconstrained and constrained many objective optimization problems. • The approach utilizes reference directions to guide the search, wherein the reference directions are generated u ...
A fast Newton`s method for a nonsymmetric - Poisson
... For this class of algebraic Riccati equations, several suitable algorithms exist for computing the minimal positive solution: the Newton method [11], the Logarithmic and Cyclic Reduction [2, 7] and the Structure-preserving Doubling Algorithm [10, 12]. All these algorithms share the same order of com ...
... For this class of algebraic Riccati equations, several suitable algorithms exist for computing the minimal positive solution: the Newton method [11], the Logarithmic and Cyclic Reduction [2, 7] and the Structure-preserving Doubling Algorithm [10, 12]. All these algorithms share the same order of com ...
Quantile Regression for Large-scale Applications
... estimates the conditional mean. The Least Absolute Deviations regression (i.e., `1 regression) is a special case of quantile regression that involves computing the median of the conditional distribution. In contrast with `1 regression and the more popular `2 or Least-squares regression, quantile reg ...
... estimates the conditional mean. The Least Absolute Deviations regression (i.e., `1 regression) is a special case of quantile regression that involves computing the median of the conditional distribution. In contrast with `1 regression and the more popular `2 or Least-squares regression, quantile reg ...
Algorithm
In mathematics and computer science, an algorithm (/ˈælɡərɪðəm/ AL-gə-ri-dhəm) is a self-contained step-by-step set of operations to be performed. Algorithms exist that perform calculation, data processing, and automated reasoning.An algorithm is an effective method that can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, eventually producing ""output"" and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.The concept of algorithm has existed for centuries, however a partial formalization of what would become the modern algorithm began with attempts to solve the Entscheidungsproblem (the ""decision problem"") posed by David Hilbert in 1928. Subsequent formalizations were framed as attempts to define ""effective calculability"" or ""effective method""; those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's ""Formulation 1"" of 1936, and Alan Turing's Turing machines of 1936–7 and 1939. Giving a formal definition of algorithms, corresponding to the intuitive notion, remains a challenging problem.