An efficient algorithm is given for the resolution of relative Thue equations. The essential improvement is the application of an appropriate version of Wildanger’s enumeration procedure based on the ellipsoid method of Fincke and Pohst. Recently relative Thue equations have gained an important application, e.g., in computing power integral bases in algebraic number fields. The presented method...

Suppose we want to minimize a polynomial p(x) = p(x1, . . . , xn), subject to some polynomial constraints q1(x), . . . , qm(x) ≥ 0, using the Sum-of-Squares (SOS) SDP hierarachy. Assume we are in the “explicitly bounded” (“Archimedean”) case where the constraints include xi ≤ 1 for all 1 ≤ i ≤ n. It is often stated that the degree-d version of the SOS hierarchy can be solved, to high accuracy, ...

In a recent paper the author 1997a] described a short algorithmic proof of a min-max theorem of E. Gy} ori 1984] on minimum generators of a system of subpaths of an underlying path. A. Frank and T. Jordd an 1995] generalized Gy} ori's theorem in several ways; the underlying path was replaced by a circuit, generators were extended to weighted generators, and minimum cost generators were also tre...

Attitude estimation is often a prerequisite for control of the attitude or orientation of mechanical systems. Current attitude estimation algorithms use coordinate representations for the group of rigid body orientations. All coordinate representations of the group of orientations have associated problems. While minimal coordinate representations exhibit kinematic singularities for large rotati...

For many target and anomaly detection algorithms, a key step is the estimation of a centroid (relatively easy) and a covariance matrix (somewhat harder) that characterize the background clutter. For a background that can be modeled as a multivariate Gaussian, the centroid and covariance lead to an explicit probability density function that can be used in likelihood ratio tests for optimal detec...

In many real-life situations, we do not know the probability distribution of measurement errors but only upper bounds on these errors. In such situations, once we know the measurement results, we can only conclude that the actual (unknown) values of a quantity belongs to some interval. Based on this interval uncertainty, we want to find the range of possible values of a desired function of the ...

A novel procedure for segmenting a set of scattered 3D data obtained from a head and shoulders multiview sequence is presented. The procedure consists of two steps. In the first step, two ellipses corresponding to the head and the body of the person are identified based on ellipse fitting of the outline of the person in each image. The fitting is based on a fast direct least squares method usin...

Noah Stein, Pablo Parrilo, and Asu Ozdaglar pointed out an error on page 10, lines 13-14 of our paper “Computing Correlated Equilibria in Multi-Player Games” (Journal of the ACM, 2008). The incorrect phrase is “...which contradicts our assumption that the violating y is within the current ellipsoid”. This conclusion would be valid for the bounding ellipsoid used for the original dual program (D...

The efficiency of a Genetic Algorithm for constrained parameter optimization depends heavily on the ratio of feasible to infeasible area in its rectangular search space. We show an algorithm based on existing mathematical programming methods which improves this ratio assuming a set of linear constraints. We approximate the feasible area by a multidimensional ellipsoid and rotate the original se...