Related papers: TRPL+K: Thick-Restart Preconditioned Lanczos+K Met…
ILU(k) is a commonly used preconditioner for iterative linear solvers for sparse, non-symmetric systems. It is often preferred for the sake of its stability. We present TPILU(k), the first efficiently parallelized ILU(k) preconditioner that…
The spectral decomposition of a real skew-symmetric matrix $A$ can be mathematically transformed into a specific structured singular value decomposition (SVD) of $A$. Based on such equivalence, a skew-symmetric Lanczos bidiagonalization…
In this paper, we address the efficient numerical solution of linear and quadratic programming problems, often of large scale. With this aim, we devise an infeasible interior point method, blended with the proximal method of multipliers,…
In this paper, we propose a novel tensor-based Dinkelbach--Type method for computing extremal tensor generalized eigenvalues. We show that the extremal tensor generalized eigenvalue can be reformulated as a critical subproblem of the…
Low-rank and nonsmooth matrix optimization problems capture many fundamental tasks in statistics and machine learning. While significant progress has been made in recent years in developing efficient methods for \textit{smooth} low-rank…
The computation of sparse solutions of large-scale linear discrete ill-posed problems remains a computationally demanding task. A powerful framework in this context is the use of iteratively reweighted schemes, which are based on…
In this paper a new restarting method for Krylov subspace matrix exponential evaluations is proposed. Since our restarting technique essentially employs the residual, some convergence results for the residual are given. We also discuss how…
Preconditioning has long been a staple technique in optimization, often applied to reduce the condition number of a matrix and speed up the convergence of algorithms. Although there are many popular preconditioning techniques in practice,…
Efficient matrix trace estimation is essential for scalable computation of log-determinants, matrix norms, and distributional divergences. In many large-scale applications, the matrices involved are too large to store or access in full,…
The discretization of the double-layer potential integral equation for the interior Dirichlet Laplace problem in a domain with smooth boundary results in a linear system that has a bounded condition number. Thus, the number of iterations…
Inhomogeneous dynamical mean-field theory has been employed to solve many interesting strongly interacting problems from transport in multilayered devices to the properties of ultracold atoms in a trap. The main computational step,…
We introduce an algorithm that is simultaneously memory-efficient and low-scaling for applying ab initio molecular Hamiltonians to matrix-product states (MPS) via the tensor-hypercontraction (THC) format. These gains carry over to Krylov…
Recent work found that an analysis formalism based on the Lanczos algorithm allows energy levels to be extracted from Euclidean correlation functions with faster ground-state convergence than effective masses, convergent estimators for…
Convex quadratic programming (QP) is an important class of optimization problem with wide applications in practice. The classic QP solvers are based on either simplex or barrier method, both of which suffer from the scalability issue…
The scaling law, which indicates that model performance improves with increasing dataset and model capacity, has fueled a growing trend in expanding recommendation models in both industry and academia. However, the advent of large-scale…
A class of restarted randomized surrounding methods are presented to accelerate the surrounding algorithms by restarted techniques for solving the linear equations. Theoretical analysis prove that the proposed method converges under the…
Spectral clustering is one of the most important algorithms in data mining and machine intelligence; however, its computational complexity limits its application to truly large scale data analysis. The computational bottleneck in spectral…
Incomplete factorization is a widely used preconditioning technique for Krylov subspace methods for solving large-scale sparse linear systems. Its multilevel variants, such as ILUPACK, are more robust for many symmetric or unsymmetric…
An iterative algorithm is presented for solving the RPA equations of linear response. The method optimally computes the energy-weighted moments of the strength function, allowing one to match the computational effort to the intrinsic…
Trust region policy optimization (TRPO) is a popular and empirically successful policy search algorithm in Reinforcement Learning (RL) in which a surrogate problem, that restricts consecutive policies to be 'close' to one another, is…