Christian E. Schaerer

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In this paper, we describe block matrix algorithms for the iterative solution of large scale linear-quadratic optimal control problems arising from the control of parabolic partial differential equations over a finite control horizon. After spatial discretization, by finite element or finite difference methods, the original problem reduces to an optimal(More)
In this paper, the 2D Haar wavelet transform is the proposed analysis technique for HTTP traffic data. Web attacks are detected by two threshold operations applied to the wavelet coefficients of the 2D transform: one based on their median and the other on the best approximation method. The two proposed algorithms are validated through an extensive number of(More)
In this paper, we describe and analyse several block matrix iterative algorithms for solving a saddle point linear system arising from the discretization of a linear-quadratic elliptic control problem with Neumann boundary conditions. To ensure that the problem is well posed, a regularization term with a parameter is included. The first algorithm reduces(More)
In this paper, we describe block matrix algorithms for the iterative solution of large scale linear-quadratic optimal control problems arising from the optimal control of parabolic partial differential equations over a finite control horizon. We describe three iterative algorithms. The first algorithm employs a CG method for solving a symmetric positive(More)
We study the use of inexact and truncated Krylov subspace methods for the solution of the linear systems arising in the discretized solution of the optimal control of a parabolic partial differential equation. An all-at-once temporal discretization and a reduction approach are used to obtain a symmetric positive definite system for the control variables(More)
We consider an elliptic optimal control problem in two dimensions, in which the control variable corresponds to the Neumann data on a boundary segment, and where the performance functional is regularized to ensure that the problem is well posed. A finite element discretization of this control problem yields a saddle point linear system, which can be reduced(More)
Mathematical morphology, based on lattice theory, is a nonlinear technique. In color image processing, it is necessary to determine a color space and an ordering to obtain a lattice structure. The classical lexicographical ordering is a total ordering where the choice of the main color component is not a trivial issue. In this work, to avoid this choice, a(More)
We describe a block matrix iterative algorithm for solving a linearquadratic parabolic optimal control problem (OCP) on a finite time interval. We derive a reduced symmetric indefinite linear system involving the control variables and auxiliary variables, and solve it using a preconditioned MINRES iteration, with a symmetric positive definite block diagonal(More)