Concerning decomposition of a system of linear algebraic equations
Krzysztof Moszyński (1995)
Applicationes Mathematicae
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Krzysztof Moszyński (1995)
Applicationes Mathematicae
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Víctor Álvarez, José Andrés Armario, María Dolores Frau, Félix Gudiel (2015)
Open Mathematics
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An n by n skew-symmetric type (-1; 1)-matrix K =[ki;j ] has 1’s on the main diagonal and ±1’s elsewhere with ki;j =-kj;i . The largest possible determinant of such a matrix K is an interesting problem. The literature is extensive for n ≡ 0 mod 4 (skew-Hadamard matrices), but for n ≡ 2 mod 4 there are few results known for this question. In this paper we approach this problem constructing cocyclic matrices over the dihedral group of 2t elements, for t odd, which are equivalent to (-1;...
L. Popov (2004)
Open Mathematics
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For a linear complementarity problem with inconsistent system of constraints a notion of quasi-solution of Tschebyshev type is introduced. It’s shown that this solution can be obtained automatically by Lemke’s method if the constraint matrix of the original problem is copositive plus or belongs to the intersection of matrix classes P 0 and Q 0.
Wanka, A. (1989)
Séminaire Lotharingien de Combinatoire [electronic only]
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Milan Práger (1994)
Banach Center Publications
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An iterative procedure containing two parameters for solving linear algebraic systems originating from the domain decomposition technique is proposed. The optimization of the parameters is investigated. A numerical example is given as an illustration.
Neuwirth, Erich (2002)
Séminaire Lotharingien de Combinatoire [electronic only]
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A. R. Moghaddamfar, S. M. H. Pooya, S. Navid Salehy, S. Nima Salehy (2012)
Matematički Vesnik
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M. Preiß, J. Stoer (2003)
Control and Cybernetics
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M. O. Omeike, A. U. Afuwape (2010)
Kragujevac Journal of Mathematics
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Bajalinov, E., Rácz, A. (2009)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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Guntram Scheithauer, Johannes Terno (1995)
Applicationes Mathematicae
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Many numerical computations reported in the literature show only a small difference between the optimal value of the one-dimensional cutting stock problem (1CSP) and that of the corresponding linear programming relaxation. Moreover, theoretical investigations have proven that this difference is smaller than 2 for a wide range of subproblems of the general 1CSP.
William F. Trench (2014)
Special Matrices
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Let P ∈ ℂmxm and Q ∈ ℂn×n be invertible matrices partitioned as P = [P0 P1 · · · Pk−1] and Q = [Q0 Q1 · · · Qk−1], with P ℓ ∈ ℂm×mℓ and Qℓ ∈ ℂn×nℓ , 0 ≤ ℓ ≤ k − 1. Partition P−1 and Q−1 as [...] where P̂ℓ ∈ ℂmℓ ×m, Q̂ℓ ∈ ℂnℓ×n , P̂ℓPm = δℓmImℓ , and Q̂ℓQm = δℓmInℓ , 0 ≤ ℓ, m ≤ k − 1. Let Zk = {0, 1, . . . , k − 1}. We study matrices A = [...] Pσ(ℓ)FℓQℓ and B = [...] QℓGℓPσ(ℓ), where σ : Zk → Zk. Special cases: A = [...] and B = [...] , where Aℓ ∈ ℂd1×d2 and Bℓ ∈ ℂd2×d1, 0 ≤ ℓ ≤ k − 1. ...