In the context of Krylov methods for solving systems of linear equations, expressions and bounds are derived for the norm of the minimal residual, like the one produced by GMRES or MINRES. It is shown that the minimal residual norm is large as long as the Krylov basis is well-conditioned. In the context of non-normal matrices, examples are given where the minimal residual norm is a function of ...

The goal of coded distributed computation is to efficiently distribute a task, such as matrix multiplication, N-linear computation, or multivariate polynomial evaluation, across S servers through coding scheme, that the response from any R ( called recovery threshold) sufficient for user recover desired computed value. Current state-of-art approaches are based on either exclusively matrix-parti...

ABSTRACT. For parameters n, l and r, we consider the problem of maximizing the determinant of an l × l Vandermonde matrix V, with nodes selected from the set Ωn of nth roots of unity, but avoiding a forbidden subset R of size r. An asymptotically tight lower bound is given for the expected value of ln |detV | in case the nodes are selected uniformly at random from Ωn/R. We apply our result to g...

Singular spectral analysis has recently become an attractive tool in a broad range of applications. Its main mechanism of alternating between rank reduction and Hankel projection, however, deserves further mathematical justification. Exploiting a natural parametrization of a general Hankel matrix via its Vandermonde factorization, this paper recasts the numerical scheme for the singular spectra...

This letter presents a new computational tool for use in general fading channel analyses when the detection scheme can be expressed as a quadratic form in zero-mean complex Gaussian random variables. We develop a simple numerical algorithm which is capable of inverting a characteristic function consisting of both simple and multiple poles. The approach benefits from the inherent symmetry in the...

We consider an N-dimensional real integral, indexed by a parameter that specifies the power of a Vandermonde determinant. For two particular values of the parameter, this integral arises from matrix integrals, over real symmetric and complex Hermitian N × N matrices. When it is normalized, it gives the expectation of an arbitrary power of the determinant. The results are given as finite summati...

In this paper, we consider methods to compute the coefficients of interpolants relative to a basis of polynomials satisfying a three-term recurrence relation. Two new algorithms are presented: the first constructs the coefficients of the interpolation incrementally and can be used to update the coefficients whenever a nodes is added to or removed from the interpolation. The second algorithm, wh...

A set T ⊂ GF(q), q = ph is a super-Vandermonde set if ∑y∈T yk = 0 for 0 < k < |T |. We determine the structure of super-Vandermonde sets of size p + 1 (almost small) and size q/p − 1 (almost large).