An Efficient Gauss-Newton Algorithm for Symmetric Low-Rank Product Matrix Approximations

We derive and study a Gauss-Newton method for computing a symmetric low-rank product that is the closest to a given symmetric matrix in Frobenius norm. Our Gauss-Newton method, which has a particularly simple form, shares the same order of iteration-complexity as a gradient method when the size of desired eigenspace is small, but can be … Read more

Limited Memory Block Krylov Subspace Optimization for Computing Dominant Singular Value Decompositions

In many data-intensive applications, the use of principal component analysis (PCA) and other related techniques is ubiquitous for dimension reduction, data mining or other transformational purposes. Such transformations often require efficiently, reliably and accurately computing dominant singular value decompositions (SVDs) of large unstructured matrices. In this paper, we propose and study a subspace optimization technique … Read more