We consider sparse (or toric) elimination theory in order to describe, by combinatorial means, the monomials appearing in the (sparse) resultant of a given overconstrained algebraic system. A modification of reverse search allows us to enumerate all mixed cell configurations of the given Newton polytopes so as to compute the extreme monomials of the Newton polytope of the resultant. We consider...

This paper studies the convergence properties of the well known K-Means clustering algorithm. The K-Means algorithm can be described either as a gradient descent algorithm or by slightly extending the mathematics of the EM algorithm to this hard threshold case. We show that the K-Means algorithm actually minimizes the quantization error using the very fast Newton algorithm.

Resultants are defined in the sparse (or toric) context in order to exploit the structure of the polynomials as expressed by their Newton polytopes. Since determinantal formulae are not always possible, the most efficient general method for computing resultants is as the ratio of two determinants. This is made possible by Macaulay’s seminal result [15] in the dense homogeneous case, extended by...

This paper studies the convergence properties of the well known K Means clustering algorithm The K Means algorithm can be de scribed either as a gradient descent algorithm or by slightly extend ing the mathematics of the EM algorithm to this hard threshold case We show that the K Means algorithm actually minimizes the quantization error using the very fast Newton algorithm

In this paper, we present the Gauss-Newton method as a unified approach to estimating noise parameters of the prevalent non-linear compensation models, such as vector Taylor series (VTS), data-driven parallel model combination (DPMC), and unscented transform (UT), for noise-robust speech recognition. While iterative estimation of noise means in a generalized EM framework has been widely known, ...

In this paper a second-order method for solving large-scale strongly convex `1-regularized problems is developed. The proposed method is a NewtonCG (Conjugate Gradients) algorithm with backtracking line-search embedded in a doubly-continuation scheme. Worst-case iteration complexity of the proposed Newton-CG is established. Based on the analysis of Newton-CG, worstcase iteration complexity of t...

An efficient multi-block Newton–Krylov algorithm using the compressible Navier–Stokes equations is presented for the analysis and design of high-lift airfoil configurations. The preconditioned generalized minimum residual (GMRES) method is applied to solve the discreteadjoint equation, leading to a fast computation of accurate objective function gradients. Furthermore, the GMRES method is used ...

We compare the performance of several robust large-scale minimization algorithms applied for the minimization of the cost functional in the solution of ill-posed inverse problems related to parameter estimation applied to the parabolized Navier-Stokes equations. The methods compared consist of the conjugate gradient method (CG), Quasi-Newton (BFGS), the limited memory Quasi-Newton (L-BFGS) [1],...

Newton's method for solving the matrix equation F(X) identical to AX-XX(T) AX = 0 runs up against the fact that its zeros are not isolated. This is due to a symmetry of F by the action of the orthogonal group. We show how differential-geometric techniques can be exploited to remove this symmetry and obtain a "geometric" Newton algorithm that finds the zeros of F. The geometric Newton method doe...

We describe the implementation details and give the experimental results of three optimization algorithms for dense optical flow computation. In particular, using a line search strategy, we evaluate the performance of the unilevel truncated Newton method (LSTN), a multiresolution truncated Newton (MR/LSTN) and a full multigrid truncated Newton (FMG/LSTN). We use three image sequences and four m...