Related papers: An Alternative to Vinberg's Algorithm
In this paper, we generalize Spencer's hyperbolic cosine algorithm to the matrix-valued setting. We apply the proposed algorithm to several problems by analyzing its computational efficiency under two special cases of matrices; one in which…
Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference…
In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6068] this problem is approached by alternating minimization…
Variational quantum algorithms (VQAs) have emerged in recent years as a promise to obtain quantum advantage. These task-oriented algorithms work in a hybrid loop combining a quantum processor and classical optimization. Using a specific…
A new algorithm for one-dimensional minimization is described in detail and the results of some tests on practical cases are reported and illustrated. The method requires only punctual computation of the function, and is suitable to be…
Wigner functions play a central role in the phase space formulation of quantum mechanics. Although closely related to classical Liouville densities, Wigner functions are not positive definite and may take negative values on subregions of…
We give an algorithm for solving equations and inequations with rational constraints in virtually free groups. Our algorithm is based on Rips classification of measured band complexes. Using canonical representatives, we deduce an algorithm…
Recenty Abrams and Lloyd have proposed a fast algorithm that is based on a nonlinear evolution of a state of a quantum computer. They have explicitly used the fact that nonlinear evolutions in Hilbert spaces do not conserve scalar products…
Variational methods are highly valuable computational tools for solving high-dimensional quantum systems. In this paper, we explore the effectiveness of three variational methods: the density matrix renormalization group (DMRG), Boltzmann…
In a recent paper, Kuperberg described the first subexponential time algorithm for solving the dihedral hidden subgroup problem. The space requirement of his algorithm is super-polynomial. We describe a modified algorithm whose running time…
It is believed that some numerical technique must be employed for the determination of the system parameters of a visual binary or a star with a planet because the relevant equations are not only highly nonlinear but also transcendental…
We exhibit an explicit, deterministic algorithm for finding a canonical form for a positive definite matrix under unimodular integral transformations. We use characteristic sets of short vectors and partition-backtracking graph software.…
A hyperbolic reflection group is a discrete group generated by reflections in the faces of an $n$-dimensional hyperbolic polyhedron. This survey article is dedicated to the study of arithmetic hyperbolic reflection groups with an emphasis…
We introduce the Binary Matrix Guessing Problem and provide two algorithms to solve this problem. The first algorithm we introduce is Elementwise Probing Algorithm (EPA) which is very fast under a score which utilizes Frobenius Distance.…
We consider frequency-weighted damping optimization for vibrating systems described by a second-order differential equation. The goal is to determine viscosity values such that eigenvalues are kept away from certain undesirable areas on the…
Hyperbolic polynomials is a class of real-roots polynomials that has wide range of applications in theoretical computer science. Each hyperbolic polynomial also induces a hyperbolic cone that is of particular interest in optimization due to…
An alternative numerical method is developed to find stable and unstable periodic orbits of nonlinear dynamical systems. The method exploits the high-efficiency of the Levenberg-Marquardt algorithm for medium-sized problems and has the…
We present a constructive recognition algorithm to decide whether a given black-box group is isomorphic to an alternating or a symmetric group without prior knowledge of the degree. This eliminates the major gap in known algorithms, as they…
The characterization of quantum features in large Hilbert spaces is a crucial requirement for testing quantum protocols. In the continuous variables encoding, quantum homodyne tomography requires an amount of measurements that increases…
An alternative method is described for determining the hyperbolic structure on a link complement, and some of its elementary consequences are examined. The method is particularly suited to alternating links.