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Sobol’ sequences (also called LP τ sequences or (t, s) sequences in base 2) are a type of quasi-random low-discrepancy sequence.They were first introduced by the Russian mathematician Ilya M. Sobol’ (Илья Меерович Соболь) in 1967.
An interior point method was discovered by Soviet mathematician I. I. Dikin in 1967. [1] The method was reinvented in the U.S. in the mid-1980s. In 1984, Narendra Karmarkar developed a method for linear programming called Karmarkar's algorithm, [2] which runs in probably polynomial time (() operations on L-bit numbers, where n is the number of variables and constants), and is also very ...
A maximum length sequence (MLS) is a type of pseudorandom binary sequence.. They are bit sequences generated using maximal linear-feedback shift registers and are so called because they are periodic and reproduce every binary sequence (except the zero vector) that can be represented by the shift registers (i.e., for length-m registers they produce a sequence of length 2 m − 1).
Given a prime number q and prime power q m with positive integers m and d such that d ≤ q m − 1, a primitive narrow-sense BCH code over the finite field (or Galois field) GF(q) with code length n = q m − 1 and distance at least d is constructed by the following method.
An intuitive explanation of the algorithm from "Numerical Recipes": [5] The downhill simplex method now takes a series of steps, most steps just moving the point of the simplex where the function is largest (“highest point”) through the opposite face of the simplex to a lower point.
ML involves the study and construction of algorithms that can learn from and make predictions on data. [3] These algorithms operate by building a model from a training set of example observations to make data-driven predictions or decisions expressed as outputs, rather than following strictly static program instructions.
Suppose that there is an underlying signal {x(t)}, of which an observed signal {r(t)} is available.The observed signal r is related to x via a transformation that may be nonlinear and may involve attenuation, and would usually involve the incorporation of random noise.
All algorithms that work this way are referred to as Krylov subspace methods; they are among the most successful methods currently available in numerical linear algebra. These methods can be used in situations where there is an algorithm to compute the matrix-vector multiplication without there being an explicit representation of A ...