Related papers: Derivation of fast DCT algorithms using algebraic …
The usage of linear transformations has great relevance for data decorrelation applications, like image and video compression. In that sense, the discrete Tchebichef transform (DTT) possesses useful coding and decorrelation properties. The…
With the wide application of spectral and algebraic theory in discrete signal processing techniques in the field of graph signal processing, an increasing number of signal processing methods have been proposed, such as the graph Fourier…
The damped Gauss-Newton (dGN) algorithm for CANDECOMP/PARAFAC (CP) decomposition can handle the challenges of collinearity of factors and different magnitudes of factors; nevertheless, for factorization of an $N$-D tensor of size $I_1\times…
We describe algorithms to compute fixed fields, splitting fields and towers of radical extensions without using polynomial factorisation in towers or constructing any field containing the splitting field, instead extending Galois group…
We point out the relevance of the Differential Galois Theory of linear differential equations for the exact semiclassical computations in path integrals in quantum mechanics. The main tool will be a necessary condition for complete…
We develop differential calculus and gauge theory on a finite set G. An elegant formulation is obtained when G is supplied with a group structure and in particular for a cyclic group. Connes' two-point model (which is an essential…
The present paper essentially contains two results that generalize and improve some of the constructions of [arXiv:0801.1493]. First of all, in the case of one derivation, we prove that the parameterized Galois theory for difference…
Functional graphs (FGs) model the graph structures used to analyse the behaviour of functions from a discrete set to itself. In turn, such functions are used to study real complex phenomena evolving in time. As the systems involved can be…
While algebrisation constitutes a powerful technique in the design and analysis of centralised algorithms, to date there have been hardly any applications of algebraic techniques in the context of distributed graph algorithms. This work is…
A Galois theory of differential fields with parameters is developed in a manner that generalizes Kolchin's theory. It is shown that all connected differential algebraic groups are Galois groups of some appropriate differential field…
This is a collection of example computations that are cited in the Appendix of [DNT]. In each case, the aim is to show that the extension of a given finite simple group by an elementary abelian group of given rank has the property that not…
A new class of integrable maps, obtained as lattice versions of polynomial dynamical systems is introduced. These systems are obtained by means of a discretization procedure that preserves several analytic and algebraic properties of a…
We describe an efficient algorithm for computing the matrix vector products that appear in the numerical resolution of boundary integral equations in 2 space dimension. This work is an extension of the so-called Sparse Cardinal Sine…
We present a distributed anytime algorithm for performing MAP inference in graphical models. The problem is formulated as a linear programming relaxation over the edges of a graph. The resulting program has a constraint structure that…
We use the well-known observation that the solutions of Jacobi's differential equation can be represented via non-oscillatory phase and amplitude functions to develop a fast algorithm for computing multi-dimensional Jacobi polynomial…
In this paper we propose a generic algorithm to calculate the rotation parameters of CORDIC angles required for the Discrete Cosine Transform algorithm (DCT). This leads us to increase the precision of calculation meeting any accuracy.Our…
The main motivation of our work is to create an efficient algorithm that decides hypertranscendence of solutions of linear differential equations, via the parameterized differential and Galois theories. To achieve this, we expand the…
In this paper, we develop an efficient decoder via the proximal alternating direction method of multipliers (proximal-ADMM) technique for nonbinary linear block codes in the Galois field. Its main contents are as follows: first, exploiting…
The discrete cosine transform (DCT) is the key step in many image and video coding standards. The 8-point DCT is an important special case, possessing several low-complexity approximations widely investigated. However, 16-point DCT…
We develop an algorithm for the computation of general Fourier integral operators associated with canonical graphs. The algorithm is based on dyadic parabolic decomposition using wave packets and enables the discrete approximate evaluation…