相关论文: An effective Procedure for Speeding up Algorithms

A general condition determining the optimal performance of a complex system has not yet been found and the possibility of its existence is unknown. To contribute in this direction, an optimization algorithm as a complex system is presented.…

The expectation-maximization (EM) algorithm is a well-known iterative method for computing maximum likelihood estimates from incomplete data. Despite its numerous advantages, a main drawback of the EM algorithm is its frequently observed…

This paper describes a fast algorithm for transforming Legendre coefficients into Chebyshev coefficients, and vice versa. The algorithm is based on the fast multipole method and is similar to the approach described by Alpert and Rokhlin…

We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase in comparison to the fastest known…

The convergence rate of various first-order optimization algorithms is a pivotal concern within the numerical optimization community, as it directly reflects the efficiency of these algorithms across different optimization problems. Our…

Many learning algorithms are formulated in terms of finding model parameters which minimize a data-fitting loss function plus a regularizer. When the regularizer involves the l0 pseudo-norm, the resulting regularization path consists of a…

We present a new strongly polynomial algorithm for generalized flow maximization that is significantly simpler and faster than the previous strongly polynomial algorithm [V\'egh16]. For the uncapacitated problem formulation, the complexity…

In nearly every discipline, scientific computations are limited by the cost and speed of computation. For example, the best-known exact algorithms for the canonical Traveling Salesman Problem would take centuries to run on an instance of…

Deep learning methods are useful for high-dimensional data and are becoming widely used in many areas of software engineering. Deep learners utilizes extensive computational power and can take a long time to train-- making it difficult to…

We consider iterative gradient-based optimization algorithms applied to functions that are smooth and strongly convex. The fastest globally convergent algorithm for this class of functions is the Triple Momentum (TM) method. We show that if…

People solve different problems and know that some of them are simple, some are complex and some insoluble. The main goal of this work is to develop a mathematical theory of algorithmic complexity for problems. This theory is aimed at…

We propose an acceleration scheme for first-order methods (FOMs) for convex quadratic programs (QPs) that is analogous to Anderson acceleration and the Generalized Minimal Residual algorithm for linear systems. We motivate our proposed…

Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operations research, and optimization. Despite the consistent efforts on this problem, all…

We construct fast algorithms for evaluating transforms associated with families of functions which satisfy recurrence relations. These include algorithms both for computing the coefficients in linear combinations of the functions, given the…

We give new positive and negative results (some conditional) on speeding up computational algebraic geometry over the reals: (1) A new and sharper upper bound on the number of connected components of a semialgebraic set. Our bound is novel…

In this paper, we develop a unified framework able to certify both exponential and subexponential convergence rates for a wide range of iterative first-order optimization algorithms. To this end, we construct a family of parameter-dependent…

We propose a very simple preprocessing algorithm for semidefinite programming. Our algorithm inspects the constraints of the problem, deletes redundant rows and columns in the constraints, and reduces the size of the variable matrix. It…

In this paper, we first present an explicit expression for the inverse\emph{} of a type of matrices. As special applications, the inverse of some matrices arising from implicit time integration techniques, such as the well-known implicit…

We apply our recent work on empirical estimates of quantum speedups to the practical task of community detection in complex networks. We design several quantum variants of a popular classical algorithm -- the Louvain algorithm for community…

Quantum algorithms can potentially solve a handful of problems more efficiently than their classical counterparts. In that context, it has been discussed that Markov chains problems could be solved significantly faster using quantum…