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With the development of 3D sensing technologies, point clouds have attracted increasing attention in a variety of applications for 3D object representation, such as autonomous driving, 3D immersive tele-presence and heritage reconstruction.…
Windowed recurrences are sliding window calculations where a function is applied iteratively across the window of data, and are ubiquitous throughout the natural, social, and computational sciences. In this monograph we explore the…
We analyse and compare the complexity of several algorithms for computing modular polynomials. We show that an algorithm relying on floating point evaluation of modular functions and on interpolation, which has received little attention in…
We present normal forms for elliptic curves over a field of characteristic $2$ analogous to Edwards normal form, and determine bases of addition laws, which provide strikingly simple expressions for the group law. We deduce efficient…
Persistence diagrams, combining geometry and topology for an effective shape description used in pattern recognition, have already proven to be an effective tool for shape representation with respect to a certainfiltering function.…
With the increased availability of 3D scanning technology, point clouds are moving into the focus of computer vision as a rich representation of everyday scenes. However, they are hard to handle for machine learning algorithms due to their…
To cater to the needs of (Zero Knowledge) proofs for (mathematical) proofs, we describe a method to transform formal sentences in 2x2-matrices over multivariate polynomials with integer coefficients, such that usual proof-steps like…
In this paper, we present an algorithm for reparametrizing birational surface parametrizations into birational polynomial surface parametrizations without base points, if they exist. For this purpose, we impose a transversality condition to…
A finite-element algorithm for computing free-surface flows driven by arbitrary body forces is presented. The algorithm is primarily designed for the microfluidic parameter range where (i) the Reynolds number is small and (ii) force-driven…
An efficient and flexible engine for computing fixed points is critical for many practical applications. In this paper, we firstly present a goal-directed fixed point computation strategy in the logic programming paradigm. The strategy…
We study the structure of collections of algebraic curves in three dimensions that have many curve-curve incidences. In particular, let $k$ be a field and let $\mathcal{L}$ be a collection of $n$ space curves in $k^3$, with…
An algorithm is presented for the efficient and accurate computation of the coefficients of the characteristic polynomial of a general square matrix. The algorithm is especially suited for the evaluation of canonical traces in determinant…
The Fourier transforms of polyhedral cones can be used, via Brion's theorem, to compute various geometric quantities of polytopes, such as volumes, moments, and lattice-point counts. We present a novel method of computing these conic…
In this paper, we suggest a new efficient algorithm in order to compute S-polynomial reduction rapidly in the known algorithm for computing Grobner bases, and compare the complexity with others.
We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…
We present a new mathematical formulation to estimate the intrinsic parameters of a camera in active or robotic platforms. We show that the focal lengths can be estimated using only one point correspondence that relates images taken before…
In this paper, we will give a uniform upper bound of the number of rational points of bounded height in non-singular curves by applying the global determinant method.
An efficient algorithm for computing eigenvectors of a matrix of integers by exact computation is proposed. The components of calculated eigenvectors are expressed as polynomials in the eigenvalue to which the eigenvector is associated, as…
We analyse the complexity of computing class polynomials, that are an important ingredient for CM constructions of elliptic curves, via complex floating point approximations of their roots. The heart of the algorithm is the evaluation of…
In this paper, we present a geometric approach for computing the controlled invariant set of a continuous-time control system. While the problem is well studied for in the ellipsoidal case, this family is quite conservative for constrained…