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This article presents maximum likelihood estimators (MLEs) and log-likelihood ratio (LLR) tests for the eigenvalues and eigenvectors of Gaussian random symmetric matrices of arbitrary dimension, where the observations are independent repeated samples from one or two populations. These inference problems are relevant in the analysis of diffusion tensor… (More)

- Walter F. Mascarenhas
- Math. Program.
- 2004

This work shows that the BFGS method and other methods in the Broyden class, with exact line searches, may fail for non-convex objective functions.

- Roberto Cominetti, Walter F. Mascarenhas, Paulo J. S. Silva
- Math. Program. Comput.
- 2014

We introduce a new efficient method to solve the continuous quadratic knapsack problem. This is a highly structured quadratic program that appears in different contexts. The method converges after O(n) iterations with overall arithmetic complexity O(n2). Numerical experiments show that in practice the method converges in a small number of iterations with… (More)

- Walter F. Mascarenhas
- SIAM J. Matrix Analysis Applications
- 1995

This paper presents new results concerning the effect of the ordering on the rate of convergence of the Jacobi iteration for computing eigenvalues of symmetric matrices. We start by showing that the diagonal elements converge for any ordering. Next we emphasize that different parts of the matrix converge at different speeds. Taking advantage of this… (More)

- Walter F. Mascarenhas
- SIAM Journal on Optimization
- 1997

We present two examples in which the dual affine scaling algorithm converges to a vertex that is not optimal if at each iteration we move 0.999 of the step to the boundary of the feasible region.

We present a new stability analysis for the second barycentric formula, showing that this formula is backward stable when the relevant Lebesgue constant is small.

- Walter F. Mascarenhas
- Math. Program.
- 2008

In this note we discuss the convergence of Newton’s method for minimization. We present examples in which the Newton iterates satisfy the Wolfe conditions and the Hessian is positive definite at each step and yet the iterates converge to a non-stationary point. These examples answer a question posed by Fletcher in his 1987 book Practical methods of… (More)

A new method is introduced for packing items in convex regions of the Euclidian ndimensional space. By means of this approach the packing problem becomes a global finitedimensional continuous optimization problem. The strategy is based on the new concept of sentinels. Sentinels sets are finite subsets of the items to be packed such that, when two items are… (More)

- Walter F. Mascarenhas
- Numerische Mathematik
- 2014

- Alan Edelman, Walter F. Mascarenhas
- Numerical Lin. Alg. with Applic.
- 1995

Dedicated to our friends Beresford and Velvel on the occasion of their sixtieth birthdays. ABSTRACT We show that a certain matrix norm ratio studied by Parlett has a supremum that is O(p n) when the chosen norm is the Frobenius norm, while it is O(log n) for the 2-norm. This ratio arises in Parlett's analysis of the Cholesky decomposition of an n by n… (More)