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Computational & Applied Mathematics, Volume: 22, Número: 1, Publicado: 2003
  • Finding the closest Toeplitz matrix

    Eberle, Maria Gabriela; Maciel, Maria Cristina

    Resumo em Inglês:

    The constrained least-squares n × n-matrix problem where the feasibility set is the subspace of the Toeplitz matrices is analyzed. The general, the upper and lower triangular cases are solved by making use of the singular value decomposition. For the symmetric case, an algorithm based on the alternate projection method is proposed. The implementation does not require the calculation of the eigenvalue of a matrix and still guarantees convergence. Encouraging preliminary results are discussed.
  • A weighted projection centering method

    Moretti, Antonio Carlos

    Resumo em Inglês:

    An iterative method for finding the center of a linear programming polytope is presented. The method assumes that we start at a feasible interior point and each iterate is obtained as a convex combination of the orthogonal projection on the half spaces defined by the linear inequalities plus a special projections on the same half spaces. The algorithm is particularly suitable for implementation on computers with parallel processors. We show some examples in two dimensional space to describe geometrically how the method works. Finally, we present computational results on random generated polytopes and linear programming polytopes from NetLib to compare the centering quality of the center using projections and the analytic center approach.
  • On the convergence properties of the projected gradient method for convex optimization

    Iusem, A. N.

    Resumo em Inglês:

    When applied to an unconstrained minimization problem with a convex objective, the steepest descent method has stronger convergence properties than in the noncovex case: the whole sequence converges to an optimal solution under the only hypothesis of existence of minimizers (i.e. without assuming e.g. boundedness of the level sets). In this paper we look at the projected gradient method for constrained convex minimization. Convergence of the whole sequence to a minimizer assuming only existence of solutions has also been already established for the variant in which the stepsizes are exogenously given and square summable. In this paper, we prove the result for the more standard (and also more efficient) variant, namely the one in which the stepsizes are determined through an Armijo search.
  • A mathematical formulation of the boundary integral equations for a compressible stokes flow

    Cunha, Francisco Ricardo; Sousa, Aldo João de; Loewenberg, Michael

    Resumo em Inglês:

    A general boundary integral formulation for compressible Stokes flows is theoretically described within the framework of hydrodynamic potentials. The integral equation is implemented numerically to the study of drop expansion in compressible viscous flows. Marker point positions on the drop interface are involved by using the boundary integral method for calculation of fluid velocity. Surface discretization is adaptive to the instantaneous drops shapes. The interplay between viscous and surface tension and its influence on the evolving emulsion microstructure during its expansion is fundamental to the science and technology of foam processing. In this article the method is applied for 3D simulations of emulsion densification that involves an uniform expansion of a viscous fluid containing spherical drops on a body centered cubic lattice (BCC).
  • Optimal design of a plate of variable thickness: a variational approach in dimension one

    Pedregal, Pablo; Donoso, Alberto

    Resumo em Inglês:

    For a typical design problem of a plate of variable thickness, we analyze the one-dimensional situation through a variational reformulation to discover that, in contrast with the higher dimensional case, there are optimal solutions. Another typical interpretation of this simplification is that of the optimal shape of a bending beam. The mechanism employed for the existence issue is the direct method for the new formulation. Optimality conditions are then pursued.
  • Generalized line criterion for Gauss-Seidel method

    Garcia, M.V.P.; Humes Jr., C.; Stern, J.M.

    Resumo em Inglês:

    We present a module based criterion, i.e. a sufficient condition based on the absolute value of the matrix coefficients, for the convergence of Gauss-Seidel method (GSM) for a square system of linear algebraic equations, the Generalized Line Criterion (GLC). We prove GLC to be the ''most general'' module based criterion and derive, as GLC corollaries, some previously know and also some new criteria for GSM convergence. Although far more general than the previously known results, the proof of GLC is simpler. The results used here are related to recent research in stability of dynamical systems and control of manufacturing systems.
  • Finite element approximation of bipolar viscous fluids

    Manouzi, H.; Brahmi, A.; Farhloul, M.

    Resumo em Inglês:

    A bipolar viscous fluid model is assumed to regularise the solution of Newtonian and quasi-Newtonian flows. In this article, a mixed finite element approximation of the bipolar viscous fluids is proposed. In this approximation the velocity of the fluid together with its laplacian are the most relevant unknowns. An existence and uniqueness results are proved. A mixed finite element approximation is derived and numerical results are presented.
  • Approximate controllability for the semilinear heat equation in R N involving gradient terms

    Menezes, Silvano Bezerra de

    Resumo em Inglês:

    We prove the approximate controllability of the semilinear heat equation in R N, when the nonlinear term is globally Lipschitz and depends both on the state u and its spatial gradient <FONT FACE=Symbol>Ñ</FONT>u. The approximate controllability is viewed as the limit of a sequence of optimal control problems. In order to avoid the difficulties related to the lack of compactness of the Sobolev embeddings, we work with the similarity variables and use weighted Sobolev spaces.
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