Related papers: On efficient approximation of quadratic irrational…
Equilibrium measures are special invariant measures of chaotic dynamical systems and iterated function systems, commonly studied as salient examples of fractal measures. While useful analytic expressions are rare, computational exploration…
We present a series of algorithms for computing geometric and representation-theoretic invariants of Calogero-Moser spaces and rational Cherednik algebras associated to complex reflection groups. Especially, we are concerned with…
We give an efficient algorithm to enumerate all sets of $r\ge 1$ quadratic polynomials over a finite field, which remain irreducible under iterations and compositions.
We introduce here a general framework for studying continued fraction expansions for complex numbers and establish some results on the convergence of the corresponding sequence of convergents. For continued fraction expansions with partial…
In this work, we consider a rational approximation of the exponential function to design an algorithm for computing matrix exponential in the Hermitian case. Using partial fraction decomposition, we obtain a parallelizable method, where the…
Quadratically constrained quadratic programs (QCQPs) are an expressive family of optimization problems that occur naturally in many applications. It is often of interest to seek out sparse solutions, where many of the entries of the…
Results from studies of effective Lagrangians for gaugino condensation are summarized and re-examined with an eye to previously neglected one-loop quadratically divergent corrections.
We report results on various techniques which allow to compute the expansion into Legendre (or in general Gegenbauer) polynomials in an efficient way. We describe in some detail the algebraic/symbolic approach already presented in Ref.1 and…
In this paper, we propose a distributed algorithm for solving large-scale separable convex problems using Lagrangian dual decomposition and the interior-point framework. By adding self-concordant barrier terms to the ordinary Lagrangian, we…
We present an algorithm to compute all factorizations into linear factors of univariate polynomials over the split quaternions, provided such a factorization exists. Failure of the algorithm is equivalent to non-factorizability for which we…
A recursion formula for derivatives of Chebyshev polynomials is replaced by an explicit formula.
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…
We present a new, far simpler family of counter-examples to Kushnirenko's Conjecture. Along the way, we illustrate a computer-assisted approach to finding sparse polynomial systems with maximally many real roots, thus shedding light on the…
It has been shown numerically that the performance of the Levenberg-Marquardt algorithm can be improved by including a second order correction known as the geodesic acceleration. In this paper we give the method a more sound theoretical…
In this article, a globally convergent sequential quadratic programming (SQP) method is developed for multi-objective optimization problems with inequality type constraints. A feasible descent direction is obtained using a linear…
In this note we study some sequences whose ratio converges to the square root of rationals. Further we analyze some related sequences obtained when the above mentioned ratio simplifies.
This paper presents a novel algorithm for constructing a sum-of-squares (SOS) decomposition for positive semi-definite polynomials with rational coefficients. Unlike previous methods that typically yield SOS decompositions with…
A method for sequential inference of the fixed parameters of a dynamic latent Gaussian models is proposed and evaluated that is based on the iterated Laplace approximation. The method provides a useful trade-off between computational…
We prove that any solution of a degenerate elliptic PDE is of class $C^1$, provided the inverse of the equation's degeneracy law satisfies an integrability criterium, viz. $\sigma^{-1} \in L^1\left (\frac{1}{\lambda} {\bf d}\lambda\right…
We reprove the countable splitting lemma by adapting Nawrotzki's algorithm which produces a sequence that converges to a solution. Our algorithm combines Nawrotzki's approach with taking finite cuts. It is constructive in the sense that…