This paper presents a splatting algorithm for volume rendering of curvilinear grids. A stochastic sampling technique called Poisson sphere/ellipsoid sampling is employed to adaptively resample a curvilinear grid with a set of randomly distributed points whose energy support extents are well approximated by spheres and ellipsoids. Filter kernels corresponding to these spheres and ellipsoids are ...

Unfalsified Control is a data-driven, plant-model-free controller design method, which recursively falsifies controllers that fail to meet the specified performance requirement. In Ellipsoidal Unfalsified Control, the region of controllers that are unfalsified, the Unfalsified set, is described by an ellipsoid. Due to the combination of the performance requirement and controller structure, the ...

The best known approximation algorithm for graph MAX CUT, due to Goemans and Williamson, rst nds the optimal solution a semideenite program and then derives a graph cut from that solution. Building on this result, Karger, Motwani, and Sudan gave an approximation algorithm for graph coloring that also involves solving a semideenite program. Solving these semideenite programs using known methods ...

This paper deals with the problem of clustering a data−set. In particular, the bisecting divisive partitioning approach is here considered. We focus on two algorithms: the celebrated K−means algorithm, and the recently proposed Principal Direction Divisive Partitioning (PDDP) algorithm. A comparison of the two algorithms is given, under the assumption that the data set is uniformly distributed ...

In this work, we develop duality of the minimum volume circumscribed ellipsoid and the maximum volume inscribed ellipsoid problems. We present a unified treatment of both problems using convex semi–infinite programming. We establish the known duality relationship between the minimum volume circumscribed ellipsoid problem and the optimal experimental design problem in statistics. The duality res...

The ellipsoid algorithm tells us that given these oracles to a problem, guarantees of not too large of an initial search space, and not too small of a possible volume for P = 0, we get a polynomial solution. With this observation, we may hope to achieve polynomial algorithms to certain LP with many more constraints than the natural parameters of the problem. Specifically, if m, the number of co...

This paper deals with the problem of clustering a data set. In particular, the bisecting divisive partitioning approach is here considered. We focus on two algorithms: the celebrated K-means algorithm, and the recently proposed Principal Direction Divisive Partitioning (PDDP) algorithm. A comparison of the two algorithms is given, under the assumption that the data set is uniformly distributed ...

In this paper, we propose a concept of polynomiality for variational inequality problems and show how to find a near optimal solution of variational inequality problems in a polynomial number of iterations. To establish this result we build upon insights from several algorithms for linear and nonlinear programs (the ellipsoid algorithm, the method of centers of gravity, the method of inscribed ...

The best known approximation algorithm for graph MAX CUT, due to Goemans and Williamson, rst nds the optimal solution of a semideenite program and then derives a graph cut from that solution. Building on this result, Karger, Motwani, and Su-dan gave an approximation algorithm for graph coloring that also involves solving a semideenite program. Solving these semideenite programs using known meth...

A novel method of learning complex fuzzy decision regions in the n-dimensional feature space is proposed. Through the fuzzy decision regions, a given pattern's class membership value of every class is determined instead of the conventional crisp class the pattern belongs to. The n-dimensional fuzzy decision region is approximated by union of hyperellipsoids. By explicitly parameterizing these h...