We show that the Euclidean condition number of any positive deenite Hankel matrix of order n 3 may be bounded from below by n?1 =(16n) with = exp(4Catalan==) 3:210, and that this bound may be improved at most by a factor 8n. Similar estimates are given for the class of real Vandermonde matrices, the class of row scaled real Vandermonde matrices, and the class of Krylov matrices with Hermitian a...

The generating function for the number of purely crossing partitions of {1, . . . , n} is found in terms of the generating function for Bell numbers. Further results about generating functions for asymptotic moments of certain random Vandermonde matrices are derived.

A novel joint angle and delay estimation (JADE) algorithm for multipath signals, based on the PARAllel profiles with LINear Dependencies (PARALIND) model, is proposed. Capitalizing on the structure property of Vandermonde matrices, PARALIND model is proved to be unique. Angle and delay of multiple rays of sources can be estimated by PARALIND decomposition and an ESPRIT-like shift-invariance tec...

We present several generalizations of Cauchy’s determinant det (1/(xi + yj)) and Schur’s Pfaffian Pf ((xj − xi)/(xj + xi)) by considering matrices whose entries involve some generalized Vandermonde determinants. Special cases of our formulae include previous formulae due to S. Okada and T. Sundquist. As an application, we give a relation for the Littlewood– Richardson coefficients involving a r...

We introduce a partial order on partitions which permits an inductive proof on partitions. As an example of this technique, we reprove the discriminant formula for the generalized Vandermonde determinant.  2003 Elsevier Inc. All rights reserved.

In this thesis, we explore different algorithms for the inversion of Vandermonde matrices and the corresponding suitable architectures for implement in FPGA. The inversion of Vandermonde matrix is one of the three master projects of the topic, Implementation of a digital error correction algorithm for time-interleaved analog-to-digital converters. The project is divided into two major parts: al...

A single unicast index coding problem (SUICP) with symmetric neighboring and consecutive side-information (SNCS) has K messages and K receivers, the kth receiver Rk wanting the kth message xk and having the side-information Kk = {xk−U , . . . , xk−2, xk−1} ∪ {xk+1, xk+2, . . . , xk+D}. The single unicast index coding problem with symmetric neighboring and consecutive side-information, SUICP(SNC...

When {α i } 1≤i≤m is a sequence of distinct non-zero elements of an integral domain A and γ is a common multiple of the α i in A we obtain, by means of a simple identity for the Vandermonde determinant, a lower bound for sup 1≤i<j≤m φ(α i − α j) in terms of φ(γ), where φ is a function from the nonzero elements of A to R + satisfying certain natural conditions. We describe several applications o...

We find geometric and arithmetic conditions on a finite set of integer exponents and the characteristic of a field k in order to characterize the irreducibility of the determinant of the generic Vandermonde matrix determined by these exponents in the algebraic closure of k. Tools from Tropical Geometry are then applied in order to characterize those determinants that are irreducible over any fi...

Although Gaussian elimination uses O(n) operations to invert an arbitrary matrix, matrices with a special Vandermonde structure can be inverted in only O(n) operations by the fast Traub algorithm. The original version of Traub algorithm was numerically unstable although only a minor modification of it yields a high accuracy in practice. The Traub algorithm has been extended from Vandermonde mat...