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- Matemática (CB,MICF) - 2008/2009Publication . Conceição, Ana C.Apontamentos utilizados nas aulas teóricas da Unidade Curricular "Matemática", no ano letivo 2008/2009, para os alunos da Licenciatura em Ciências Biomédicas e do Mestrado Integrado em Ciências Farmacêuticas.
- Factorização de algumas classes de funções matriciais e suas aplicaçõesPublication . Conceição, Ana; Kravchenko, Viktor Grigorievich; Teixeira, Francisco Sepúlveda
- 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.