Related papers: A fast algorithm for computing minimal-norm soluti…

An algorithm which either finds an nonzero integer vector ${\mathbf m}$ for given $t$ real $n$-dimensional vectors ${\mathbf x}_1,...,{\mathbf x}_t$ such that ${\mathbf x}_i^T{\mathbf m}=0$ or proves that no such integer vector with norm…

Given matrices A and B and vectors a, b, c and d, all with non-negative entries, we consider the problem of computing min {c.x: x in Z^n_+, Ax > a, Bx < b, x < d}. We give a bicriteria-approximation algorithm that, given epsilon in (0, 1],…

We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…

While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…

Classically, a mainstream approach for solving a convex-concave min-max problem is to instead solve the variational inequality problem arising from its first-order optimality conditions. Is it possible to solve min-max problems faster by…

With a high probability the Sarlos randomized algorithm of 2006 outputs a nearly optimal least squares solution of a highly overdeterminedlinear system of equations. We propose its simple deterministic variation which computes such a…

We give a deterministic O(log n)^n algorithm for the {\em Shortest Vector Problem (SVP)} of a lattice under {\em any} norm, improving on the previous best deterministic bound of n^O(n) for general norms and nearly matching the bound of…

We present a randomized algorithm that, on input a symmetric, weakly diagonally dominant n-by-n matrix A with m nonzero entries and an n-vector b, produces a y such that $\norm{y - \pinv{A} b}_{A} \leq \epsilon \norm{\pinv{A} b}_{A}$ in…

We provide the currently fastest randomized (1+epsilon)-approximation algorithm for the closest vector problem in the infinity norm. The running time of our method depends on the dimension n and the approximation guarantee epsilon by 2^O(n)…

This manuscript describes a technique for computing partial rank-revealing factorizations, such as, e.g, a partial QR factorization or a partial singular value decomposition. The method takes as input a tolerance $\varepsilon$ and an…

In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested…

This article generalizes a recently introduced procedure to solve nonlinear systems of equations, radically departing from the conventional Newton-Raphson scheme. The original nonlinear system is first unfolded into three simpler…

We present classical sublinear-time algorithms for solving low-rank linear systems of equations. Our algorithms are inspired by the HHL quantum algorithm for solving linear systems and the recent breakthrough by Tang of dequantizing the…

In this work, we propose a new randomized algorithm for computing a low-rank approximation to a given matrix. Taking an approach different from existing literature, our method first involves a specific biased sampling, with an element being…

This paper proposes a new algorithm for linear system identification from noisy measurements. The proposed algorithm balances a data fidelity term with a norm induced by the set of single pole filters. We pose a convex optimization problem…

Differentiable systems in this paper means systems of equations that are described by differentiable real functions in real matrix variables. This paper proposes algorithms for finding minimal rank solutions to such systems over (arbitrary…

We present a quantum algorithm for fitting a linear regression model to a given data set using the least squares approach. Different from previous algorithms which yield a quantum state encoding the optimal parameters, our algorithm outputs…

We present a numerical algorithm for finding real non-negative solutions to polynomial equations. Our methods are based on the expectation maximization and iterative proportional fitting algorithms, which are used in statistics to find…

We present an approximation scheme for minimizing certain Quadratic Integer Programming problems with positive semidefinite objective functions and global linear constraints. This framework includes well known graph problems such as Minimum…

We propose a new algorithm for minimal unsatisfiable core extraction, based on a deeper exploration of resolution-refutation properties. We provide experimental results on formal verification benchmarks confirming that our algorithm finds…