Related papers: A Lanczos algorithm for linear response
We develop the linear response theory for the Google matrix PageRank algorithm with respect to a general weak perturbation and a numerical efficient and accurate algorithm, called LIRGOMAX algorithm, to compute the linear response of the…
Reinforcement learning (RL) excels in optimizing policies for discrete-time Markov decision processes (MDP). However, various systems are inherently continuous in time, making discrete-time MDPs an inexact modeling choice. In many…
We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…
We study the pointwise (in the space and time variables) behavior of the linearized Landau equation for hard and moderately soft potentials. The solution has very clear description in the $(x,t)-$variables, including large time behavior and…
Currently, existing tensor recovery methods fail to recognize the impact of tensor scale variations on their structural characteristics. Furthermore, existing studies face prohibitive computational costs when dealing with large-scale…
There has been significant interest and progress recently in algorithms that solve regression problems involving tall and thin matrices in input sparsity time. These algorithms find shorter equivalent of a n*d matrix where n >> d, which…
We study numerical methods for the solution of general linear moment problems, where the solution belongs to a family of nested subspaces of a Hilbert space. Multi-level algorithms, based on the conjugate gradient method and the…
One of the main subjects in the field of social networks is to quantify conflict, disagreement, controversy, and polarization, and some quantitative indicators have been developed to quantify these concepts. However, direct computation of…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
We use moment techniques to construct a converging hierarchy of optimization problems to lower bound the ground state energy of interacting particle systems. We approximate (from below) the infinite dimensional optimization problems in this…
We present a novel iterative algorithm for approximating the linear least squares solution with low complexity. After a motivation of the algorithm we discuss the algorithm's properties including its complexity, and we present theoretical…
Many real-world applications are addressed through a linear least-squares problem formulation, whose solution is calculated by means of an iterative approach. A huge amount of studies has been carried out in the optimization field to…
We give an algorithm to compute $N$ steps of a convolution quadrature approximation to a continuous temporal convolution using only $O(N \log N)$ multiplications and $O(\log N)$ active memory. The method does not require evaluations of the…
The particle-particle random phase approximation (pp-RPA) has been shown to be capable of describing double, Rydberg, and charge transfer excitations, for which the conventional time-dependent density functional theory (TDDFT) might not be…
The network Lasso (nLasso) has been proposed recently as an efficient learning algorithm for massive networked data sets (big data over networks). It extends the well-known least absolute shrinkage and selection operator (Lasso) from…
The accurate computation of non-linear optical properties (NLOPs) in large polymers requires accounting for electronic correlation effects with a reasonable computational cost. The Random Phase Approximation (RPA) used in the adiabatic…
The variational optimization of high-dimensional neural network models, such as those used in neural quantum states (NQS), presents a significant challenge in machine intelligence. Conventional first-order stochastic methods (e.g., Adam)…
We give improved algorithms for the $\ell_{p}$-regression problem, $\min_{x} \|x\|_{p}$ such that $A x=b,$ for all $p \in (1,2) \cup (2,\infty).$ Our algorithms obtain a high accuracy solution in $\tilde{O}_{p}(m^{\frac{|p-2|}{2p + |p-2|}})…
We show that the standard Lanczos algorithm can be efficiently implemented statistically and self consistently improved, using the stochastic reconfigurat ion method, which has been recently introduced to stabilize the Monte Carlo sign…
Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…