A construction is given for a planar rational Pythagorean hodograph spiral which interpolates any two-point G Hermite data that a spiral can match. When the curvature at one of the points is zero, the construction gives the unique interpolant that is the involute of a rational Pythagorean hodograph curve of the form cubic over linear. Otherwise, the spiral comprises an involute of a Tschirnhaus...

This paper discusses the rigorous enclosure of an ellipsoid by a rectangular box, its interval hull, providing a convenient preprocessing step for constrained optimization problems. A quadratic inequality constraint with a positive definite Hessian defines an ellipsoid. The Cholesky factorization can be used to transform a strictly convex quadratic constraint into a norm inequality, for which t...

Noncentral indefinite quadratic expressions in possibly non- singular normal vectors are represented in terms of the difference of two positive definite quadratic forms and an independently distributed linear combination of standard normal random variables. This result also ap- plies to quadratic forms in singular normal vectors for which no general representation is currently available. The ...

A special instance of the algebraic Riccati equation XCX−XE−AX+B = 0 where the n × n matrix coefficients A,B,C,E are rank structured matrices is considered. Relying on the structural properties of Cauchy-like matrices, an algorithm is designed for performing the customary Newton iteration in O(n2) arithmetic operations (ops). The same technique is used to reduce the cost of the algorithm propos...

Inspired by Tikhonov regularization, a non-linear conjugate gradient method is proposed with the purpose of simultaneously regularizing and solving the moment matrix equation. The procedure is based on a non-quadratic conjugate gradient algorithm with exact line search, restart and rescale. Applied to the problem of TM scattering by perfectly conducting rectangular cylinders, the method is show...

One approach to computing a square root of a matrix A is to apply Newton's method to the quadratic matrix equation F( X) = X2 A =0. Two widely-quoted matrix square root iterations obtained by rewriting this Newton iteration are shown to have excellent mathematical convergence properties. However, by means of a perturbation analysis and supportive numerical examples, it is shown that these simpl...

Title of dissertation: Adaptive Constraint Reduction for Convex Quadratic Programming and Training Support Vector Machines Jin Hyuk Jung, Doctor of Philosophy, 2008 Dissertation directed by: Professor Dianne P. O’Leary Department of Computer Science Convex quadratic programming (CQP) is an optimization problem of minimizing a convex quadratic objective function subject to linear constraints. We...

In this work we present a unified method of relative camera pose estimation from points and lines correspondences. Given a set of 2D points and lines correspondences in three views, of which two are known, a method has been developed for estimating the camera pose of the third view. Novelty of this algorithm is to combine both points and lines correspondences in the camera pose estimation which...

Abstract. We investigate the behavior of isotropic invariant subspaces of skew-Hamiltonian matrices under structured perturbations. It is shown that finding a nearby subspace is equivalent to solving a certain quadratic matrix equation. This connection is used to derive meaningful error bounds and condition numbers that can be used to judge the quality of invariant subspaces computed by strongl...

Abstract We analyze the exponential stability of distributed parameter systems. The system we consider is described by a coupled parabolic partial differential equation with spatially varying coefficients. We approximate the coefficients by splitting space domains. However, we take into account approximation errors during stability analysis. Using a quadratic Lyapunov function, we obtain a suff...