Displaying similar documents to “Equation with residuated functions”

Interpretation and optimization of the k -means algorithm

Kristian Sabo, Rudolf Scitovski (2014)

Applications of Mathematics

Similarity:

The paper gives a new interpretation and a possible optimization of the well-known k -means algorithm for searching for a locally optimal partition of the set 𝒜 = { a i ∈ ℝ n : i = 1 , ⋯ , m } which consists of k disjoint nonempty subsets π 1 , ⋯ , π k , 1 ≤ k ≤ m . For this purpose, a new divided k -means algorithm was constructed as a limit case of the known smoothed k -means algorithm. It is shown that the algorithm constructed in this way coincides with the k -means algorithm if during the iterative procedure no data points appear in the...

Derivation of BiCG from the conditions defining Lanczos' method for solving a system of linear equations

Petr Tichý, Jan Zítko (1998)

Applications of Mathematics

Similarity:

Lanczos’ method for solving the system of linear algebraic equations A x = b consists in constructing a sequence of vectors x k in such a way that r k = b - A x k ∈ r 0 + A 𝒦 k ( A , r 0 ) and r k ⊥ 𝒦 k ( A T , r ˜ 0 ) . This sequence of vectors can be computed by the BiCG (BiOMin) algorithm. In this paper is shown how to obtain the recurrences of BiCG (BiOMin) directly from this conditions.

A branch and bound algorithm for the two-machine flowshop problem with unit-time operations and time delays

Aziz Moukrim, Djamal Rebaine, Mehdi Serairi (2014)

RAIRO - Operations Research - Recherche Opérationnelle

Similarity:

In this paper we consider the problem of scheduling, on a two-machine flowshop, a set of unit-time operations subject to time delays with respect to the makespan. This problem is known to be 𝒩 P x1d4a9;x1d4ab; -hard in the strong sense. We propose an algorithm based on a branch and bound enumeration scheme. This algorithm includes the implementation of new lower and upper bound procedures, and dominance rules. A computer simulation to measure the performance of the algorithm is provided...