Related papers: A Note on Robust Biarc Computation
The singular value decomposition (SVD) is a crucial tool in machine learning and statistical data analysis. However, it is highly susceptible to outliers in the data matrix. Existing robust SVD algorithms often sacrifice speed for…
New iterative methods for solving linear equations are presented that are easy to use, generalize good existing methods, and appear to be faster. The new algorithms mix two kinds of linear recurrence formulas. Older methods have either high…
We analyze the bit complexity of an algorithm for the computation of at least one point in each connected component of a smooth real algebraic set. This work is a continuation of our analysis of the hypersurface case (On the bit complexity…
An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper-C2 objective functions is proposed and analyzed. Upper-C2 is a weakly concave property that exists in difference of convex (DC) functions and…
In this paper, we study several important geometric optimization problems arising in machine learning. First, we revisit the Minimum Enclosing Ball (MEB) problem in Euclidean space $\mathbb{R}^d$. The problem has been extensively studied…
We propose Bidirectional Shape Correspondence (BSC) as a possible improvement on the famous shape contexts (SC) framework. Our proposals derive from the observation that the SC framework enforces a one-to-one correspondence between sample…
We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which…
We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix by solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of…
The most widely used algorithm for floating point complex division, known as Smith's method, may fail more often than expected. This document presents two improved complex division algorithms. We present a proof of the robustness of the…
Matrix operations such as matrix inversion, eigenvalue decomposition, singular value decomposition are ubiquitous in real-world applications. Unfortunately, many of these matrix operations so time and memory expensive that they are…
The task of approximating points with circular arcs is performed in many applications, such as polyline compression, noise filtering, and feature recognition. However, the development of algorithms that perform a significant amount of…
We consider the task of decentralized minimization of the sum of smooth strongly convex functions stored across the nodes of a network. For this problem, lower bounds on the number of gradient computations and the number of communication…
In a previous paper it was shown that a machine learning regression problem can be solved within the framework of random function theory, with the optimal kernel analytically derived from symmetry and indifference principles and coinciding…
We propose new sequential simulation-optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. The performance of each choice of discrete decision variables is evaluated…
In geometry processing, numerical optimization methods often involve solving sparse linear systems of equations. These linear systems have a structure that strongly resembles to adjacency graphs of the underlying mesh. We observe how…
In this paper, we propose an improved numerical algorithm for solving minimax problems based on nonsmooth optimization, quadratic programming and iterative process. We also provide a rigorous proof of convergence for our algorithm under…
Solving linear systems of polynomial equations is a ubiquitous problem in both mathematics and physics. The standard approach, Gaussian elimination, scales cubically with system size and often constitutes a computational bottleneck. The…
We consider the problem of analyzing and designing gradient-based discrete-time optimization algorithms for a class of unconstrained optimization problems having strongly convex objective functions with Lipschitz continuous gradient. By…
A numerical algorithm (implemented in Matlab) for computing the zeros of the parabolic cylinder function $U(a,z)$ in domains of the complex plane is presented. The algorithm uses accurate approximations to the first zero plus a highly…
Finding the inverse of a matrix is an open problem especially when it comes to engineering problems due to their complexity and running time (cost) of matrix inversion algorithms. An optimum strategy to invert a matrix is, first, to reduce…