Matrix Inversion by Rank Annihilation

Structures preserved by matrix inversion

Department of Computer Science, K.U.Leuven Celestijnenlaan 200A B-3001 Heverlee, Belgium In this talk we investigate some matrix structures on Cn×n that have a good behaviour under matrix inversion. The first kind of structure is strongly related to low displacement rank structure. The second kind of structure deals with certain low rank submatrices. In this case, it can be shown that also the ...

A stable iteration to the matrix inversion

The matrix inversion plays a signifcant role in engineering and sciences. Any nonsingular square matrix has a unique inverse which can readily be evaluated via numerical techniques such as direct methods, decomposition scheme, iterative methods, etc. In this research article, first of all an algorithm which has fourth order rate of convergency with conditional stability will be proposed. ...

Generalized Rank Annihilation Method . 111 : Practical Implementation

Low-Rank Matrix Completion by Riemannian Optimization

The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a novel algorithm for matrix completion that minimizes the least square distance on the sampling set over the Riemannian manifold of fixed-rank matrices. The algorithm is an adaptation of classical non-linear conjugate gradients, developed within the framework o...

Discriminative Visualization by Limited Rank Matrix Learning

We propose an extension of the recently introduced Generalized Matrix Learning Vector Quantization (GMLVQ) algorithm. The original algorithm provides a discriminative distance measure of relevance factors, aided by adaptive square matrices, which can account for correlations between different features and their importance for the classification. We extend the scheme to matrices of limited rank ...