The distributed fusion filtering problem is studied for multi-rate sampling stochastic singular linear systems with multiple sensors and stochastic multiplicative noises. The system is described at the highest sampling rate and different sensors may have different lower sampling rates. The white noise in measurement matrix is introduced to describe the stochastic disturbance. Firstly, based on ...

Debbah and Ryan have recently [DR07] proved a result about the limit empirical singular distribution of the sum of two rectangular random matrices whose dimensions tend to infinity. In this paper, we reformulate it in terms of the rectangular free convolution introduced in [BG07b] and then we give a new, shorter, proof of this result under weaker hypothesis: we do not suppose the probability me...

A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination with no pivoting as well as block Gaussian elimination, approximation of the leading and trailing singular spaces of an ill conditioned matrix, associated wit...

A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination with no pivoting as well as block Gaussian elimination, approximation of the leading and trailing singular spaces of an ill conditioned matrix, associated wit...

A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination with no pivoting as well as block Gaussian elimination, approximation of the leading and trailing singular spaces of an ill conditioned matrix, associated wit...

A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination with no pivoting as well as block Gaussian elimination, approximation of the leading and trailing singular spaces of an ill conditioned matrix, associated wit...

A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination with no pivoting as well as block Gaussian elimination, approximation of the leading and trailing singular spaces of an ill conditioned matrix, associated wit...

In this paper, we provide an algorithmic method to compute the singular values of sum of rectangular matrices based on the free cumulants approach and illustrate its application to wireless communications. We first recall the algorithms working for sum/products of square random matrices, which have already been presented in some previous papers and we then introduce the main contribution of thi...

Let ∆1, . . . ,∆K be d × n matrices. We define the row product of these matrices as a d × n matrix, whose rows are entry-wise products of rows of ∆1, . . . ,∆K . This construction arises in certain computer science problems. We study the question, to which extent the spectral and geometric properties of the row product of independent random matrices resemble those properties for a d × n matrix ...