Related papers: Some algorithms related to the Jacobian Conjecture
We review properties of q-orthogonal polynomials, related to their orthogonality, duality and connection with the theory of symmetric (self-adjoint) operators, represented by a Jacobi matrix. In particular, we show how one can naturally…
The ability to efficiently infer system parameters is essential in any signal-processing task that requires fast operation. Dealing with quantum systems, a serious challenge arises due to substantial growth of the underlying Hilbert space…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
A new approach leading to the formulation of the Hamilton-Jacobi equation for field theories is investigated within the framework of jet-bundles and multi-symplectic manifolds. An algorithm associating classes of solutions to given sets of…
This paper highlights a formal connection between two families of widely used matrix factorization algorithms in numerical linear algebra. One family consists of the Jacobi eigenvalue algorithm and its variants for computing the Hermitian…
We present three families of pairs of geometrically non-isomorphic curves whose Jacobians are isomorphic to one another as unpolarized abelian varieties. Each family is parametrized by an open subset of P^1. The first family consists of…
By the nature of their construction, many statistical models for extremes result in likelihood functions that are computationally prohibitive to evaluate. This is consequently problematic for the purposes of likelihood-based inference. With…
A simply laced Dynkin diagram gives rise to a family of curves over $\mathbb{Q}$ and a coregular representation, using deformations of simple singularities and Vinberg theory respectively. Thorne has conjectured and partially proven a…
We study a method of producing approximately diagonal 1-qubit gates. For each positive integer, the method provides a sequence of gates that are defined iteratively from a fixed diagonal gate and an arbitrary gate. These sequences are…
Some general problems of Jacobian computations in non-full rank matrices are discussed in this work. In particular, the Jacobian of the Moore-Penrose inverse derived via matrix differential calculus is revisited. Then the Jacobian in the…
Given a family of rational curves depending on a real parameter, defined by its parametric equations, we provide an algorithm to compute a finite partition of the parameter space (${\Bbb R}$, in general) so that the shape of the family…
The Ramanujan Machine project predicts new continued fraction representations of numbers expressed by important mathematical constants. Generally, the value of a continued fraction is found by reducing it to a second order linear difference…
We first propose what we call the Gaussian Moments Conjecture. We then show that the Jacobian Conjecture follows from the Gaussian Moments Conjecture. We also give a counter-example to a more general statement known as the Moments Vanishing…
In Gaussian graphical models, the likelihood equations must typically be solved iteratively. We investigate two algorithms: A version of iterative proportional scaling which avoids inversion of large matrices, and an algorithm based on…
We propose quantum algorithms, purely quantum in nature, for calculating the determinant and inverse of an $(N-1)\times (N-1)$ matrix (depth is $O(N^2\log N)$) which is a simple modification of the algorithm for calculating the determinant…
We provide a rounding error analysis of a mixed-precision preconditioned Jacobi algorithm, which uses low precision to compute the preconditioner, applies it at high precision (amounting to two matrix-matrix multiplications) and solves the…
Jacobi-type algorithms for simultaneous approximate diagonalization of real (or complex) symmetric tensors have been widely used in independent component analysis (ICA) because of their good performance. One natural way of choosing the…
Let $q \in (0,1)$ and $\delta \in (0,1)$ be real numbers, and let $C$ be a coin that comes up heads with an unknown probability $p$, such that $p \neq q$. We present an algorithm that, on input $C$, $q$, and $\delta$, decides, with…
The problem of estimating the probability of a random process reaching a certain level is well known. In this article, two-sided estimates are established for the probability that a regenerative process reaches a high level. Two auxiliary…
In the design of greedy algorithms for the maximum cardinality matching problem the utilization of degree information when selecting the next edge is a well established and successful approach. We define the class of "degree sensitive"…