相关论文: A Lanczos algorithm for linear response

Interior-point algorithms constitute a very interesting class of algorithms for solving linear-programming problems. In this paper we study efficient implementations of such algorithms for solving the linear program that appears in the…

For the \textsc{Minkowski Sum Selection} problem with linear objective functions, we obtain the following results: (1) optimal $O(n\log n)$ time algorithms for $\lambda=1$; (2) $O(n\log^2 n)$ time deterministic algorithms and expected…

We study the universal properties of the Lanczos algorithm applied to finite-size many-body quantum systems. Focusing on autocorrelation functions of local operators and on their infinite-time behaviour at finite size, we conjecture that in…

A simple iteration methodology for the solution of a set of a linear algebraic equations is presented. The explanation of this method is based on a pure geometrical interpretation and pictorial representation. Convergence using this method…

In this paper we present a comprehensive framework for learning robust low-rank representations by combining and extending recent ideas for learning fast sparse coding regressors with structured non-convex optimization techniques. This…

We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…

We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our…

Planning with a learned model remains a key challenge in model-based reinforcement learning (RL). In decision-time planning, state representations are critical as they must support local cost computation while preserving long-horizon…

Robust principal component analysis (RPCA) has drawn significant attentions due to its powerful capability in recovering low-rank matrices as well as successful appplications in various real world problems. The current state-of-the-art…

We present a new efficient algortithm for construction of linear latent structure (LLS) models. This algorithm reduces a problem of estimation of model parameters to a sequence of problems of linear algebra, which assures a low…

We present an iterative algorithm for solving a class of \\nonlinear Laplacian system of equations in $\tilde{O}(k^2m \log(kn/\epsilon))$ iterations, where $k$ is a measure of nonlinearity, $n$ is the number of variables, $m$ is the number…

RANSAC and its variants are widely used for robust estimation, however, they commonly follow a greedy approach to finding the highest scoring model while ignoring other model hypotheses. In contrast, Iteratively Reweighted Least Squares…

We propose a novel quantum algorithm for solving linear optimization problems by quantum-mechanical simulation of the central path. While interior point methods follow the central path with an iterative algorithm that works with successive…

The Lanczos method is one of the standard approaches for computing a few eigenpairs of a large, sparse, symmetric matrix. It is typically used with restarting to avoid unbounded growth of memory and computational requirements. Thick-restart…

This article deals with the adaptive and approximative computation of the Lam\'e equations. The equations of linear elasticity are considered as boundary integral equations and solved in the setting of the boundary element method (BEM).…

The Reactive Optimal Power Flow (ROPF) problem consists in computing an optimal power generation dispatch for an alternating current transmission network that respects power flow equations and operational constraints. Some means of action…

In the Range Minimum Query (RMQ) problem, we are given an array $A$ of $n$ numbers and we are asked to answer queries of the following type: for indices $i$ and $j$ between $0$ and $n-1$, query $\text{RMQ}_A(i,j)$ returns the index of a…

In this paper we propose a new iterative method to hierarchically compute a relatively large number of leftmost eigenpairs of a sparse symmetric positive matrix under the multiresolution operator compression framework. We exploit the…

Iterative algorithms are ubiquitous in the field of data mining. Widely known examples of such algorithms are the least mean square algorithm, backpropagation algorithm of neural networks. Our contribution in this paper is an improvement…

Linear regression in $\ell_p$-norm is a canonical optimization problem that arises in several applications, including sparse recovery, semi-supervised learning, and signal processing. Generic convex optimization algorithms for solving…