7 An n-dimensional joint uniform distribution is defined as a distribution whose one-dimensional marginals are uniform on some interval I. This interval is taken to be [0,1] or, when more convenient [− 1 2 , 1 2 ]. The specification of joint uniform distributions 9 in a way which captures intuitive dependence structures and also enables sampling routines is considered. The question whether ever...

For the low rank approximation of time-dependent data matrices and of solutions to matrix differential equations, an increment-based computational approach is proposed and analyzed. In this method, the derivative is projected onto the tangent space of the manifold of rank-r matrices at the current approximation. With an appropriate decomposition of rank-r matrices and their tangent matrices, th...

In this paper, we investigate the numerical error propagation and provide systematic backward stability analysis for some hierarchical rank structured matrix algorithms. We prove the backward stability of various important hierarchically semiseparable (HSS) methods, such as HSS matrix-vector multiplications, HSS ULV linear system solutions, HSS linear least squares solutions, HSS inversions, an...

in this paper‎, ‎we study the extremal‎ ‎ranks and inertias of the hermitian matrix expression $$‎ ‎f(x,y)=c_{4}-b_{4}y-(b_{4}y)^{*}-a_{4}xa_{4}^{*},$$ where $c_{4}$ is‎ ‎hermitian‎, ‎$*$ denotes the conjugate transpose‎, ‎$x$ and $y$ satisfy‎ ‎the following consistent system of matrix equations $a_{3}y=c_{3}‎, ‎a_{1}x=c_{1},xb_{1}=d_{1},a_{2}xa_{2}^{*}=c_{2},x=x^{*}.$ as‎ ‎consequences‎, ‎we g...

We are focused on numerical methods for decomposing a multivariate polynomial as a sum of univariate polynomials in linear forms. The main tool is the recent result on correspondence between the Waring rank of a homogeneous polynomial and the rank of a partially known quasi-Hankel matrix constructed from the coefficients of the polynomial. Based on this correspondence, we show that the original...