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- Factorization algorithm for some special non-rational matrix functionsPublication . Conceição, Ana C.; Kravchenko, Viktor; Pereira, José; Ball, J. A.; Bolotnikov, V.; Helton, J. W.; Rodman, L.; Spitkovsky, I. M.We construct an algorithm that allows us to determine an effective generalized factorization of a special class of matrix functions. We use the same algorithm to analyze the spectrum of a self-adjoint operator which is related to the obtained generalized factorization.
- Factorization of matrix functions and the resolvents of certain operatorsPublication . Conceição, Ana C.; Kravchenko, Viktor; Teixeira, Francisco S.; Bottcher, A.; Kaashoek, M. A.; Lebre, A. B.; DosSantos, A. F.; Speck, F. O.The explicit factorization of matrix functions of the form Agamma(b) = ( (e)(b*) (b)(b*b)(+ gammae)), where b is an n x n matrix function, a represents the identity matrix, and gamma is a complex constant, is studied. To this purpose some relations between a factorization of A, and the resolvents of the self-adjoint operators N+ (b) = P(+)bP(-)b*P+ and N- (b) = P(-)b*P(+)bP(-) are analyzed. The main idea is to show that if b is a matrix function that can be represented through the decomposition b = b(-) + b(+) where at least one of the summands is a rational matrix, then it is possible to construct an algorithm that allows us to determine an effective canonical factorization of the matrix function A(gamma).
- Factorization of some classes of matrix functions and the resolvent of a Hankel operatorPublication . Conceição, Ana C.; Kravchenko, Viktor; Teixeira, Francisco S.; Samko, S.; Lebre, A.; DosSantos, A. F.The factorization of some classes of matrix-valued functions is obtained, which yields some new results for a special class of Hankel integral operators in L-2(+). For each of its elements, it is shown that the resolvent operator can be explicitly determined through a matrix factorization obtained by solving two non-homogeneous equations.
- Factorization algorithm for some special matrix functionsPublication . Conceição, Ana C.; Kravchenko, Viktor; Bastos, M. A.; Gohberg, I.; Lebre, A. B.; Speck, F. O.We will see that it is possible to construct an algorithm that allows us to determine an effective factorization of some matrix functions. For those matrix functions it is shown that its explicit factorization can be obtained through the solutions of two non-homogeneous equations.
- About explicit factorization of some classes of non-rational matrix functionsPublication . Conceição, Ana C.; Kravchenko, ViktorWe construct an algorithm that allows us to determine an effective canonical factorization of some non-rational matrix-valued functions. For those matrix-valued functions whose entries can be represented through a innerouter factorization (when the outer function is rational) it is shown that its explicit factorization can be obtained through the solutions of two non-homogeneous equations.
- On a "stability" in the linear complementarity problemPublication . Pires, Marília; Kravchenko, ViktorIn this work we rewrote the linear complementarity problem in a formulation based on unknown projector operators. In particular, this formulation allows the introduction of a concept of "stability" that, in a certain way, might explain the way block pivotal algorithm performs. (c) 2008 Elsevier Inc. All rights reserved.