Finding a rank-maximizing matrix block

Finding Near Rank Deficiency in Matrix Products

Finding a low-rank basis in a matrix subspace

For a given matrix subspace, how can we find a basis that consists of low-rank matrices? This is a generalization of the sparse vector problem. It turns out that when the subspace is spanned by rank-1 matrices, the matrices can be obtained by the tensor CP decomposition. For the higher rank case, the situation is not as straightforward. In this work we present an algorithm based on a greedy pro...

Finding Low-rank Solutions to Matrix Problems, Efficiently and Provably

A rank-r matrix X ∈ Rm×n can be written as a product UV >, where U ∈ Rm×r andV ∈ Rn×r. One could exploit this observation in optimization: e.g., consider the minimizationof a convex function f(X) over rank-r matrices, where the scaffold of rank-r matrices is modeledvia the factorization in U and V variables. Such heuristic has been widely used before forspecific problem inst...

AN ALGORITHM FOR FINDING THE EIGENPAIRS OF A SYMMETRIC MATRIX

The purpose of this paper is to show that ideas and techniques of the homotopy continuation method can be used to find the complete set of eigenpairs of a symmetric matrix. The homotopy defined by Chow, Mallet- Paret and York [I] may be used to solve this problem with 2""-n curves diverging to infinity which for large n causes a great inefficiency. M. Chu 121 introduced a homotopy equation...

A Matrix Rank Problem