Related papers: Calculation of extended gcd by normalization
We study the convergence of a variant of distributed gradient descent (DGD) on a distributed low-rank matrix approximation problem wherein some optimization variables are used for consensus (as in classical DGD) and some optimization…
Error-tolerant graph matching gathers an important family of problems. These problems aim at finding correspondences between two graphs while integrating an error model. In the Graph Edit Distance (GED) problem, the insertion/deletion of…
The geometric multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared…
In this paper we present a unified method for solving general polynomial equations of degree less than five.
This paper introduces a new global optimization algorithm for solving the generalized linear multiplicative problem (GLMP). The algorithm starts by introducing $\bar{p}$ new variables and applying a logarithmic transformation to convert the…
We first propose a concise singular value decomposition of dual matrices. Then, the randomized version of the decomposition is presented. It can significantly reduce the computational cost while maintaining the similar accuracy. We analyze…
A problem based on the Extended Euclidean Algorithm applied to a class of polynomials with many factors is presented and believed to be hard. If so, it is a one-way function well suited for applications in digital signicatures.
Using gradient descent (GD) with fixed or decaying step-size is a standard practice in unconstrained optimization problems. However, when the loss function is only locally convex, such a step-size schedule artificially slows GD down as it…
We present a generalized algorithm based on a spherical harmonics expansion method for efficient computation of the three-dimensional gravitational potential on a multi-patch grid in spherical geometry. Instead of solving for the…
We introduce several generalizations of classical computer science problems obtained by replacing simpler objective functions with general submodular functions. The new problems include submodular load balancing, which generalizes load…
A generalized conditional gradient method for minimizing the sum of two convex functions, one of them differentiable, is presented. This iterative method relies on two main ingredients: First, the minimization of a partially linearized…
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…
Algorithms for computing rational generating functions of solutions of one-dimensional difference equations are well-known and easy to implement. We propose an algorithm for computing rational generating functions of solutions of…
In this paper, we study two general classes of optimization algorithms for kernel methods with convex loss function and quadratic norm regularization, and analyze their convergence. The first approach, based on fixed-point iterations, is…
Our paper "Solving Third Order Linear Difference Equations in Terms of Second Order Equations" gave two algorithms for solving difference equations in terms of lower order equations: an algorithm for absolute factorization, and an algorithm…
Algorithmic approach to the problem of linearization by point transformation of ordinary differential equation of arbitrary order is presented. Test-linearization is purely algorithmic.
A coarse grid correction (CGC) approach is proposed to enhance the efficiency of the matrix exponential and $\varphi$ matrix function evaluations. The approach is intended for iterative methods computing the matrix-vector products with…
We propose a new algorithm to approximate the Earth Mover's distance (EMD). Our main idea is motivated by the theory of optimal transport, in which EMD can be reformulated as a familiar $L_1$ type minimization. We use a regularization which…
The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…
Generalized linear model with $L_1$ and $L_2$ regularization is a widely used technique for solving classification, class probability estimation and regression problems. With the numbers of both features and examples growing rapidly in the…