In this first part, analytical methods for finding moments of random Vandermonde matrices are developed. Vandermonde Matrices play an important role in signal processing and communication applications such as direction of arrival estimation, precoding or sparse sampling theory for example. Within this framework, we extend classical freeness results on random matrices with i.i.d entries and show...

A new class of codes was proposed recently for perfect multi-user interference (MUI) suppression in Code Division Multiple Access (CDMA) systems. These so called Lagrange-Vandermonde (LV) codes o er deterministic MUI elimination without channel estimation, and convert frequency selective channels into at fading channels. In this work, we develop dual CDMA transceivers, naturally termed Vandermo...

Multipoint polynomial evaluation and interpolation are fundamental for modern algebraic and numerical computing. The known algorithms solve both problems over any field by using O(N log N) arithmetic operations for the input of size N , but the cost grows to quadratic for numerical solution. Our study results in numerically stable algorithms that use O(uN log N) arithmetic time for approximate ...

We exhibit confluent and effectively weakly normalizing (thus decidable) rewriting systems for the full equational theory underlying cartesian closed categories, and for polymorphic extensions of it. The λ-calculus extended with surjective pairing has been well-studied in the last two decades. It is not confluent in the untyped case, and confluent in the typed case. But to the best of our knowl...