Related papers: On Cornacchia's Algorithm
An extremely simple, description of Karmarkar's algorithm with very few technical terms is given.
Monte Carlo sampling is a powerful toolbox of algorithmic techniques widely used for a number of applications wherein some noisy quantity, or summary statistic thereof, is sought to be estimated. In this paper, we survey the literature for…
Withdrawn; replaced by longer, more detailed paper quant-ph/0010065.
This is a concise mathematical introduction to Monte Carlo methods, a rich family of algorithms with far-reaching applications in science and engineering. Monte Carlo methods are an exciting subject for mathematical statisticians and…
Given a learning task where the data is distributed among several parties, communication is one of the fundamental resources which the parties would like to minimize. We present a distributed boosting algorithm which is resilient to a…
We show that a straightforward rewrite of a known minimal polynomial algorithm yields a simpler version of a recent algorithm of A. Salagean.
The goal of this paper is to introduce ideas and methodology of the generic case complexity to cryptography community. This relatively new approach allows one to analyze the behavior of an algorithm on ''most'' inputs in a simple and…
We introduce a new replicable boosting algorithm which significantly improves the sample complexity compared to previous algorithms. The algorithm works by doing two layers of majority voting, using an improved version of the replicable…
A formalism specifying efficient, "emergent" descriptions of experimental systems is developed. It does not depend on an a priori assumption of limited available data.
In this note we give some remarks and improvements on a recent paper of us [3] about an optimization problem for the $p-$Laplace operator that were motivated by some discussion the authors had with Prof. Cianchi.
We propose an ensemble algorithm, which provides a new approach for evaluating and summing up a set of function samples. The proposed algorithm is not a quantum algorithm, insofar it does not involve quantum entanglement. The query…
We observe that successive applications of known results from the theory of positive systems lead to an {\it efficient general algorithm} for positive realizations of transfer functions. We give two examples to illustrate the algorithm, one…
People usually regard algorithms as more abstract than the programs that implement them. The natural way to formalize this idea is that algorithms are equivalence classes of programs with respect to a suitable equivalence relation. We argue…
We propose an algorithm that test membership for regular expressions and show that the algorithm is correct. This algorithm is written in the style of a sequent proof system. The advantage of this algorithm over traditional ones is that the…
Algorithm design is a laborious process and often requires many iterations of ideation and validation. In this paper, we explore automating algorithm design and present a method to learn an optimization algorithm, which we believe to be the…
The purpose of this article is to present, in a simple way, an analytic approach to special numbers and polynomials. The approach is based on the derivative polynomials. The paper is, to some extent, a review article, although it contains…
We increasingly depend on a variety of data-driven algorithmic systems to assist us in many aspects of life. Search engines and recommender systems amongst others are used as sources of information and to help us in making all sort of…
Online learning to rank is a sequential decision-making problem where in each round the learning agent chooses a list of items and receives feedback in the form of clicks from the user. Many sample-efficient algorithms have been proposed…
A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order…
The binary Euclidean algorithm is a variant of the classical Euclidean algorithm. It avoids multiplications and divisions, except by powers of two, so is potentially faster than the classical algorithm on a binary machine. We describe the…