This paper analyzes linear least squares problems with absolute quadratic constraints. We develop a generalized theory following Bookstein’s conic-fitting and Fitzgibbon’s direct ellipse-specific fitting. Under simple preconditions, it can be shown that a minimum always exists and can be determined by a generalized eigenvalue problem. This problem is numerically reduced to an eigenvalue problem...

In this paper we present a novel technique for wavelet-based corner detection using singular value decomposition (SVD). Here SVD facilitates the selection of global natural scale in discrete wavelet transform. We define natural scale as the level associated with most prominent (dominant) eigenvalue. Eigenvector corresponding to dominant eigenvalue is considered as the natural scale. The corners...

In this paper we present a novel technique for wavelet-based corner detection using singular value decomposition (SVD). Here SVD facilitates the selection of global natural scale in discrete wavelet transform. We de®ne natural scale as the level associated with most prominent (dominant) eigenvalue. Eigenvector corresponding to dominant eigenvalue is considered as the optimal scale. The corners ...

Many challenging problems in automatic control may be cast as optimization programs subject to matrix inequality constraints. Here we investigate an approach which converts such problems into non-convex eigenvalue optimization programs and makes them amenable to non-smooth analysis techniques like bundle or cutting plane methods. We prove global convergence of a first-order bundle method for pr...

given four complex matrices a, b, c and d where a 2 cnn and d 2 cmm andlet the matrix(a bc d)be a normal matrix and assume that  is a given complex number that is not eigenvalue of matrix a. we present a method to calculate the distance norm (with respect to 2-norm) from d to the set of matrices x 2 cmm such that,  be a multiple eigenvalue of matrix(a bc x). we also nd the nearest matrix ...

In this paper we consider the stabilisability of dynamical systems via time-delayed state and output feedback control. Based on an eigenvalue optimisation approach in combination with a continuation argument and a result characterising properties of the optimum eigenvalue configurations, we obtain explicit expressions for stabilisability boundaries for two-dimensional systems. As time-delayed f...

We consider large scale ill-conditioned linear systems arising from discretization of ill-posed problems. Regularization is imposed through an (assumed known) upper bound constraint on the solution. An iterative scheme, requiring the computation of the smallest eigenvalue and corresponding eigenvector, is used to determine the proper level of regularization. In this paper we consider several co...

An approach to schedule development in project management is proposed based on models and methods of idempotent algebra. The approach offers a way to represent various types of precedence relationships among activities in projects as linear vector equations in terms of an idempotent semiring. As a result, many issues in project scheduling reduce to solving computational problems in the idempote...

The problem of finding the global minimum of a multivariate polynomial can be approached by the matrix method of Stetter-Möller, which reformulates it as a large eigenvalue problem. The linear operators involved in this approach are studied using the theory of nD-systems. This supports the efficient application of iterative methods for solving eigenvalue problems such as Arnoldi methods and Jac...