The problem of gridless direction arrival (DOA) estimation is addressed in the non-uniform array (NUA) case. Traditionally, DOA and root-MUSIC are only applicable for measurements from a uniform linear (ULA). This because sample covariance matrix ULA has Toeplitz structure, both algorithms based on Vandermonde decomposition matrix. breaks into its harmonic components, which DOAs estimated. Firs...

A code symbol of a linear code is said to have locality r if this symbol could be recovered by at most r other code symbols. An (n, k, r) locally repairable code (LRC) with all symbol locality is a linear code with length n, dimension k, and locality r for all symbols. Recently, there are lots of studies on the bounds and constructions of LRCs, most of which are essentially based on the generat...

Following recent interest by the community, scaling of minimal singular value a Vandermonde matrix with nodes forming clusters on length scale Rayleigh distance complex unit circle is studied. Using approximation theoretic properties exponential sums, we show that decay only single in size largest cluster, and bound holds for arbitrary small separation distance. We also obtain generalization we...

We present a new multivariate interpolation algorithm over arbitrary fields which is primarily suited for small finite fields. Given function values at arbitrary t points, we show that it is possible to find an n-variable interpolating polynomial with at most t terms, using the number of field operations that is polynomial in t and n. The algorithm exploits the structure of the multivariate gen...

In this paper we propose a new fast O(n) algorithm for solving Cauchy linear systems of equations. An a priori rounding error analysis, which provides bounds for the forward, backward and residual errors associated with the computed solution, indicates that for the class of totally positive Cauchy matrices the proposed algorithm is forward and backward stable, producing a remarkably high relati...

Fast algorithms for computing the product by a vector are presented for a number of classes of matrices whose properties relate to the properties of Toeplitz, Vandermonde or Cauchy matrices (these matrices are de ned using the concept of displacement of a matrix) and also for their inverses. All the actions which are not dependent upon the coordinates of the input vector are singled out in a se...

In order to evaluate some quantities in Gaussian ensembles, we investigate ”vandermonde ensemble” which represents the distribution of eigenvalues of GUE in the phase space. We derive the integral equation of the level density of vandermonde ensemble and we compute the level density numerically.