The discrete cosine transform (DCT) offers superior energy compaction properties for a large class of functions and has been employed as a standard tool in many signal and image processing applications. However, it suffers from spurious behavior in the vicinity of edge discontinuities in piecewise smooth signals. To leverage the sparse representation provided by the DCT, in this article, we der...

An algorithm is considered, and shown to lead to various unusual and unique series expansions of formal Laurent series, as the sums of reciprocals of polynomials. The degrees of approximation by the rational functions which are the partial sums of these series are investigated. The types of series corresponding to rational functions themselves are also partially characterized.

This article considers a distributed reinforcement learning problem for decentralized linear quadratic (LQ) control with partial state observations and local costs. We propose zero-order policy optimization algorithm (ZODPO) that learns controllers in fashion, leveraging the ideas of gradient, optimization, consensus algorithms. In ZODPO, each agent estimates global cost by consensus, then cond...

It is often the case that the exact moments of a continuous distribution whose support is confined to a closed interval can be explicitly determined, while its exact density function either does not lend itself to numerical evaluation or proves to be mathematically intractable. A representation of a least-squares approximating polynomial which does not rely on orthogonal polynomials, is obtaine...

We prove that if f is increasing on [ 1,1], then for each n = 1, 2 . . . . . there is an increasing algebraic polynomial P. of degree n such that {f(x) P.(x){ < cw2( f, V/I x 2 /n) , where w2 is the second-order modulus of smoothness. These results complement the classical pointwise estimates of the same type for unconstrained polynomial approximation. Using these results, we characterize the m...

It is known that point searching in basic semialgebraic sets and the search for globally minimal points in polynomial optimization tasks can be carried out using (s d)O(n) arithmetic operations, where n and s are the numbers of variables and constraints and d is the maximal degree of the polynomials involved. We associate to each of these problems an intrinsic system degree which becomes in wor...