Related papers: Calculation of extended gcd by normalization
The Euclidean algorithm is one of the oldest algorithms known to mankind. Given two integral numbers $a_1$ and $a_2$, it computes the greatest common divisor (gcd) of $a_1$ and $a_2$ in a very elegant way. From a lattice perspective, it…
A fast algorithm for counting intersections of two normal curves on a triangulated surface is proposed. It yields a convenient way for treating mapping class groups of punctured surfaces by presenting mapping classes by matrices, and the…
We give a generalized definition of stretch that simplifies the efficient construction of low-stretch embeddings suitable for graph algorithms. The generalization, based on discounting highly stretched edges by taking their $p$-th power for…
We address the problem of solving strongly convex and smooth minimization problems using stochastic gradient descent (SGD) algorithm with a constant step size. Previous works suggested to combine the Polyak-Ruppert averaging procedure with…
Minimax problems have recently attracted a lot of research interests. A few efforts have been made to solve decentralized nonconvex strongly-concave (NCSC) minimax-structured optimization; however, all of them focus on smooth problems with…
Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…
Generalised planning (GP) refers to the task of synthesising programs that solve families of related planning problems. We introduce a novel, yet simple method for GP: given a set of training problems, for each problem, compute an optimal…
While Computerized Tomography (CT) images can help detect disease such as Covid-19, regular CT machines are large and expensive. Cheaper and more portable machines suffer from errors in geometry acquisition that downgrades CT image quality.…
This paper deals with convex nonsmooth optimization problems. We introduce a general smooth approximation framework for the original function and apply random (accelerated) coordinate descent methods for minimizing the corresponding smooth…
Geodesic distances on manifolds have numerous applications in image processing, computer graphics and computer vision. In this work, we introduce an approach called `LGGD' (Learned Generalized Geodesic Distances). This method involves…
In this paper it is shown that the compact linearization approach, that has been previously proposed only for binary quadratic problems with assignment constraints, can be generalized to arbitrary linear equations with positive coefficients…
This manuscript presents a new extended linear system for integral equation based techniques for solving boundary value problems on locally perturbed geometries. The new extended linear system is similar to a previously presented technique…
Conventional learning methods simplify the bilinear model by regarding two intrinsically coupled factors independently, which degrades the optimization procedure. One reason lies in the insufficient training due to the asynchronous gradient…
It is well known that the affine matrix rank minimization problem is NP-hard and all known algorithms for exactly solving it are doubly exponential in theory and in practice due to the combinational nature of the rank function. In this…
We present a fast algorithm for the total variation regularization of the $3$-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved…
In this paper, we consider the convex, finite-sum minimization problem with explicit convex constraints over strongly connected directed graphs. The constraint is an intersection of several convex sets each being known to only one node. To…
In this paper, the compact linearization approach originally proposed for binary quadratic programs with assignment constraints is generalized to such programs with arbitrary linear equations and inequalities that have positive coefficients…
We consider approximation algorithms for the problem of finding $x$ of minimal norm $\|x\|$ satisfying a linear system $\mathbf{A} x = \mathbf{b}$, where the norm $\|\cdot \|$ is arbitrary and generally non-Euclidean. We show a simple…
We consider stochastic gradient methods under the interpolation regime where a perfect fit can be obtained (minimum loss at each observation). While previous work highlighted the implicit regularization of such algorithms, we consider an…
The Column Subset Selection Problem provides a natural framework for unsupervised feature selection. Despite being a hard combinatorial optimization problem, there exist efficient algorithms that provide good approximations. The drawback of…