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Abstract: This paper analyzes the randomized error in the sense for eigenvalue and eigenvector estimation by methods based on Krylov information. In particular, the randomized analysis of the power method presented in previous works [1, 2, 11] for real symmetric matrices is generalized to normal matrices. For positive definite matrices we give a randomized algorithm for computing the condition number...
Abstract: We formulate and solve explicitly a linear programming problem that arises from the problem of choosing an internal financial law of a given financial project such that the associated discount vector maximizes a linear objective function. If the original problem has optimal solutions, then it is equivalent to a knapsack problem. We obtain its basic optimal solutions in closed form. After...
Abstract: We draw a comparison between two numerical methods to solve a magnetostatic problem set on a bounded convex domain. The problem is of vector Poisson type and is associated with boundary conditions set on the curl of the unknown, here the magnetic field. These boundary conditions therefore introduce a coupling between the components. One of the two algorithms under consideration consists...
Abstract:In this paper we propose a new a posteriori error estimator for a boundary element solution related to a Dirichlet problem with a second order elliptic partial differential operator. The method is based on an approximate solution of a boundary integral equation of the second kind by a Neumann series to estimate the error of a previously computed boundary element solution. For this one may...
Abstract:An approach to the numerical computation of the optimal feedback law for nonlinear infinite time horizon control problems is presented and tested. For a sequence of control systems with truncated time horizon the canonical equations are solved by an adapted multiple shooting algorithm. Interpolation of computed costates gives a feedback law on a prescribed region of the state space. Numerical...
Abstract:Adaptive mesh design based on a posteriori error control is studied for finite element discretisations for variational problems of Signorini type. The techniques to derive residual based error estimators developed, e.g., in ([2, 10, 20]) are extended to variational inequalities employing a suitable adaptation of the duality argument [17]. By use of this variational argument weighted a posteriori...
Abstract: Lanczos tridiagonalization processes transform a matrix into an equivalent tridiagonal one. In this paper, we propose several ways of implementing these procedures. They are based on different choices of the auxiliary polynomials which appear in the underlying theory of formal orthogonal polynomials and on a change in their normalization. We also give transpose-free variants of Lanczos processes...
Abstract: In a recent series of papers (see Goldman [13]), B-splines of negative degree were introduced and partially investigated. The main purpose of the present paper is to continue and to extend these investigations. In the first part, we look more deeply onto the negative degree B-splines; we present an explicit representation for them, as well as a degree elevation formula; this solves a problem...
Abstract: In this paper we propose an inf-sup test to identify and measure the stability of various finite element methods for the solution of multi-dimensional convection-diffusion problem.
Abstract:The Discontinuous Galerkin (DG) time-stepping method for the numerical solution of initial value ODEs is analyzed in the context of the hp-version of the Galerkin method. New a priori error bounds explicit in the time steps and in the approximation orders are derived and it is proved that the DG method gives spectral and exponential accuracy for problems with smooth and analytic time dependence,...
Abstract: In this paper, an attempt has been made to carry over known results for the finite element Galerkin method for a time dependent parabolic equation with nonsmooth initial data to an integro-differential equation of parabolic type. More precisely, for the homogeneous problem a standard energy technique in conjunction with a duality argument is used to obtain an L2-error estimate of order ...
Abstract: The object of this note is to correct an error in defining the basis for some nonconforming finite element methods when quadrilaterals occur in the partition of a two-dimensional domain.
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