A quadratically convergent Newton method for computing the polar decomposition of a full-rank matrix is presented and analysed. Acceleration parameters are introduced so as to enhance the initial rate of convergence and it is shown how reliable estimates of the optimal parameters may be computed in practice. To add to the known best approximation property of the unitary polar factor, the Hermit...

ÐThe aim of this paper is to accelerate division, square root, and square root reciprocal computations when the Goldschmidt method is used on a pipelined multiplier. This is done by replacing the last iteration by the addition of a correcting term that can be looked up during the early iterations. We describe several variants of the Goldschmidt algorithm, assuming 4-cycle pipelined multiplier, ...

The question of the existence and uniqueness of an M-matrix which is a square root of an M-matrix is discussed. The results are then used to derive some new necessary and sufficient conditions for a real matrix with nonpositive off diagonal elements to be an M-matrix.

We consider the problem of computing square root a perturbation scaled identity matrix, , where and are matrices with . This arises in various applications, including computer vision optimization methods for machine learning. derive new formula th that involves weighted sum powers matrix is particularly attractive root, since has just one term when also class Newton iterations exploit low-rank ...

We develop the Sparse Approximate Matrix Multiply (SpAMM) n-body solver for first order Newton Schulz iteration of the matrix square root and inverse square root. The solver performs recursive two-sided metric queries on a modified Cauchy-Schwarz criterion (octree-occlusion-culling in the ijkcube), yielding a bounded relative error in the matrix-matrix product and reduced complexity for problem...

The article focuses on the linear estimation problems of unknown rectangular matrices, which are solutions matrix equations with right-hand sides belonging to bounded sets. random errors observation vector have zero mathematical expectation, and correlation is belongs one two Explicit expressions guaranteed root mean square estimates for operators acting from space matrices into some given. Gua...

In simulation studies in statistics, there are many situations that we need to generate data from a multivariate normal distribution. By multivariate normal data we mean joint observations of p variables Y1, Y2, . . . , Yp, in which each individual variable by itself is normally distributed, the variables are mutually correlated, and come from a joint multivariate normal distribution. The proce...