Related papers: Algorithmic Solution for Systems of Linear Equatio…
We present a randomized linear-space solver for general linear systems $\mathbf{A} \mathbf{x} = \mathbf{b}$ with $\mathbf{A} \in \mathbb{Z}^{n \times n}$ and $\mathbf{b} \in \mathbb{Z}^n$, without any assumption on the condition number of…
We consider the fundamental problem of solving quadratic systems of equations in $n$ variables, where $y_i = |\langle \boldsymbol{a}_i, \boldsymbol{x} \rangle|^2$, $i = 1, \ldots, m$ and $\boldsymbol{x} \in \mathbb{R}^n$ is unknown. We…
Automatic algorithms attempt to provide approximate solutions that differ from exact solutions by no more than a user-specified error tolerance. This paper describes an automatic, adaptive algorithm for approximating the solution to a…
In this paper, given a linear system of equations A x = b, we are finding locations in the plane to place objects such that sending waves from the source points and gathering them at the receiving points solves that linear system of…
Matrix factorization (MF) has been widely used to discover the low-rank structure and to predict the missing entries of data matrix. In many real-world learning systems, the data matrix can be very high-dimensional but sparse. This poses an…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
This paper provides an algorithmic framework for obtaining fast distributed algorithms for a highly-dynamic setting, in which *arbitrarily many* edge changes may occur in each round. Our algorithm significantly improves upon prior work in…
Deliberating on large or continuous state spaces have been long standing challenges in reinforcement learning. Temporal Abstraction have somewhat made this possible, but efficiently planing using temporal abstraction still remains an issue.…
We propose a new class of short matrix recurrences for the solution of nonsymmetric linear equations of the type $\mathbf{A}_1\mathbf{X}\mathbf{B}_1+\ldots+\mathbf{A}_p\mathbf{X}\mathbf{B}_p=CD^T$. These iterative methods combine local…
A highly recurrent traditional bottleneck in applied mathematics, for which the most popular codes (Mathematica and Matlab) do not offer a solution, is to find all the real solutions of a system of N nonlinear equations in a certain finite…
This paper proposes distributed algorithms for multi-agent networks to achieve a solution in finite time to a linear equation $Ax=b$ where $A$ has full row rank, and with the minimum $l_1$-norm in the underdetermined case (where $A$ has…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
The maximum bipartite matching problem is among the most fundamental and well-studied problems in combinatorial optimization. A beautiful and celebrated combinatorial algorithm of Hopcroft and Karp (1973) shows that maximum bipartite…
We consider two kinds of problems: the computation of polynomial and rational solutions of linear recurrences with coefficients that are polynomials with integer coefficients; indefinite and definite summation of sequences that are…
Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still…
We consider the speed planning problem for a robotic manipulator. In particular, we present an algorithm for finding the time-optimal speed law along an assigned path that satisfies velocity and acceleration constraints and respects the…
The Kaczmarz method is an iterative method for solving large systems of equations that projects iterates orthogonally onto the solution space of each equation. In contrast to direct methods such as Gaussian elimination or QR-factorization,…
Many problems are NP-hard and, unless P = NP, do not admit polynomial-time exact algorithms. The fastest known exact algorithms exactly usually take time exponential in the input size. Much research effort has gone into obtaining faster…
Matrices with the displacement structures of circulant, Toeplitz, and Hankel types as well as matrices with structures generalizing these types are omnipresent in computations of sciences and engineering. In this paper, we present efficient…
We give a new general approach for designing exact exponential-time algorithms for subset problems. In a subset problem the input implicitly describes a family of sets over a universe of size n and the task is to determine whether the…