Related papers: Targeted Fibonacci Exponentiation
The Kaczmarz method for solving linear systems of equations is an iterative algorithm that has found many applications ranging from computer tomography to digital signal processing. Despite the popularity of this method, useful theoretical…
We describe a novel analogue algorithm that allows the simultaneous factorization of an exponential number of large integers with a polynomial number of experimental runs. It is the interference-induced periodicity of "factoring"…
The nonperturbative Hamiltonian eigenvalue problem for bound states of a quantum field theory is formulated in terms of Dirac's light-front coordinates and then approximated by the exponential-operator technique of the many-body…
We study how we can adapt a predictor to a non-stationary environment with advises from multiple experts. We study the problem under complete feedback when the best expert changes over time from a decision theoretic point of view. Proposed…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
Motivated by the training of Generative Adversarial Networks (GANs), we study methods for solving minimax problems with additional nonsmooth regularizers. We do so by employing \emph{monotone operator} theory, in particular the…
Modular exponentiation (ME) operators are one of the fundamental components of Shor's algorithm, and the place where most of the quantum resources are deployed. I propose a method for constructing the ME operators that relies upon the…
Stochastic differential equations are widely used in various fields; in particular, the usefulness of duality relations has been demonstrated in some models such as population models and Brownian momentum processes. In this study, a…
We develop a general method for incentive-based programming of hybrid quantum-classical computing systems using reinforcement learning, and apply this to solve combinatorial optimization problems on both simulated and real gate-based…
This article is about a problem in the numerical analysis of random operators. We study a version of the finite section method for the approximate solution of equations $Ax=b$ in infinitely many variables, where $A$ is a random Jacobi…
Quantum search/amplitude amplification algorithms are designed to be able to amplify the amplitude in the target state linearly with the number of operations. Since the probability is the square of the amplitude, this results in the success…
A new type of combinations of Bernstein operators is given in [1]. Here, we introduce another one, which can be used to approximate the functions with singularities. The direct and inverse results of the weighted approximation of this new…
The Randomized Kaczmarz Algorithm is a randomized method which aims at solving a consistent system of over determined linear equations. This note discusses how to find an optimized randomization scheme for this algorithm, which is related…
The Tensor-Train (TT) format is a highly compact low-rank representation for high-dimensional tensors. TT is particularly useful when representing approximations to the solutions of certain types of parametrized partial differential…
Quantum computational approaches to some classic target identification and localization algorithms, especially for radar images, are investigated, and are found to raise a number of quantum statistics and quantum measurement issues with…
Quantum computing has emerged as a promising alternative for solving combinatorial optimization problems. The standard approach for encoding optimization problems on quantum processing units (QPUs) involves transforming them into their…
We investigate a connection between generalized Fibonacci numbers and renewal theory for stochastic processes. Using Blackwell's renewal theorem we find an approximation to the generalized Fibonacci numbers. With the help of error estimates…
All known elimination techniques for (first-order) algorithmic differentiation (AD) rely on Jacobians to be given for a set of relevant elemental functions. Realistically, elemental tangents and adjoints are given instead. They can be…
Let A be a matrix, c be any linear objective function and x be a fractional vector, say an LP solution to some discrete optimization problem. Then a recurring task in theoretical computer science (and in approximation algorithms in…
Anderson acceleration (AA) is a technique for accelerating the convergence of fixed-point iterations. In this paper, we apply AA to a sequence of functions and modify the norm in its internal optimization problem to the $\mathcal{H}^{-s}$…