### A center of a polytope: An expository review and a parallel implementation.

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In this contribution, we propose a new hybrid method for minimization of nonlinear least squares. This method is based on quasi-Newton updates, applied to an approximation $A$ of the Jacobian matrix $J$, such that ${A}^{T}f={J}^{T}f$. This property allows us to solve a linear least squares problem, minimizing $\parallel Ad+f\parallel $ instead of solving the normal equation ${A}^{T}Ad+{J}^{T}f=0$, where $d\in {R}^{n}$ is the required direction vector. Computational experiments confirm the efficiency of the new method.

We address in this article the computation of the convex solutions of the Dirichlet problem for the real elliptic Monge − Ampère equation for general convex domains in two dimensions. The method we discuss combines a least-squares formulation with a relaxation method. This approach leads to a sequence of Poisson − Dirichlet problems and another sequence of low dimensional algebraic eigenvalue problems of a new type. Mixed finite element approximations with a smoothing procedure are used for the...

This paper is motivated by the paper [3], where an iterative method for the computation of a matrix inverse square root was considered. We suggest a generalization of the method in [3]. We give some sufficient conditions for the convergence of this method, and its numerical stabillity property is investigated. Numerical examples showing that sometimes our generalization converges faster than the methods in [3] are presented.

We present an easy-to-implement algorithm for transforming a matrix to rational canonical form.