Displaying similar documents to “Equation with residuated functions”

Interpretation and optimization of the k -means algorithm

Kristian Sabo, Rudolf Scitovski (2014)

Applications of Mathematics

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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

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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

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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...

Variations on the Gram-Schmidt and the Huang algorithms for linear systems: A numerical study

Emilio Spedicato, Maria Teresa Vespucci (1993)

Applications of Mathematics

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In this paper we compare the numerical performance on a set of ill conditioned problems of several algorithms for linear systems based upon the explicit QR factorization and the implicit LQ factorization associated with the Huang and the modified Huang algorithms in the ABS class. The results indicate that the modified Huang algorithm is generally more accurate than the Huang algorithm and competitive with commercial codes based upon the QR factorization with Householder of Givens reflections....