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The definition of a KZ-reduced basis was given by Aleksandr Korkin and Yegor Ivanovich Zolotarev in 1877, a strengthened version of Hermite reduction. The first algorithm for constructing a KZ-reduced basis was given in 1983 by Kannan. [2] The block Korkine-Zolotarev (BKZ) algorithm was introduced in 1987. [3]
An early successful application of the LLL algorithm was its use by Andrew Odlyzko and Herman te Riele in disproving Mertens conjecture. [5]The LLL algorithm has found numerous other applications in MIMO detection algorithms [6] and cryptanalysis of public-key encryption schemes: knapsack cryptosystems, RSA with particular settings, NTRUEncrypt, and so forth.
Lattice reduction in two dimensions: the black vectors are the given basis for the lattice (represented by blue dots), the red vectors are the reduced basis. In mathematics, the goal of lattice basis reduction is to find a basis with short, nearly orthogonal vectors when given an integer lattice basis as input. This is realized using different ...
The reduced form of the system is: = + = +, with vector of reduced form errors that each depends on all structural errors, where the matrix A must be nonsingular for the reduced form to exist and be unique. Again, each endogenous variable depends on potentially each exogenous variable.
The process of feature selection aims to find a suitable subset of the input variables (features, or attributes) for the task at hand.The three strategies are: the filter strategy (e.g., information gain), the wrapper strategy (e.g., accuracy-guided search), and the embedded strategy (features are added or removed while building the model based on prediction errors).
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Extensions so far are a desktop-version to run reduced models and initial support for KerMor kernel-based reduced models is on the way. MORLAB: Model Order Reduction Laboratory. This toolbox is a collection of MATLAB/OCTAVE routines for model order reduction of linear dynamical systems based on the solution of matrix equations.
The reduced Gröbner basis of the unit is formed by the single polynomial 1. In the case of polynomials in a single variable, there is a unique admissible monomial ordering, the ordering by the degree. The minimal Gröbner bases are the singletons consisting of a single polynomial. The reduced Gröbner bases are the monic polynomials.