Related papers: A survey of subspace recycling iterative methods
This work is concerned with approximating matrix functions for banded matrices, hierarchically semiseparable matrices, and related structures. We develop a new divide-and-conquer method based on (rational) Krylov subspace methods for…
Subspace clustering methods based on expressing each data point as a linear combination of all other points in a dataset are popular unsupervised learning techniques. However, existing methods incur high computational complexity on…
A standard approach to reduced-order modeling of higher-order linear dynamical systems is to rewrite the system as an equivalent first-order system and then employ Krylov-subspace techniques for reduced-order modeling of first-order…
We consider algebraic iterative reconstruction methods with applications in image reconstruction. In particular, we are concerned with methods based on an unmatched projector/backprojector pair; i.e., the backprojector is not the exact…
Transformers have recently gained prominence in long time series forecasting by elevating accuracies in a variety of use cases. Regrettably, in the race for better predictive performance the overhead of model architectures has grown…
Primal and dual block coordinate descent methods are iterative methods for solving regularized and unregularized optimization problems. Distributed-memory parallel implementations of these methods have become popular in analyzing large…
We present a novel data-driven reformulation of the iterative SVD-rational Krylov algorithm (ISRK), in its original formulation a Petrov-Galerkin (two-sided) projection-based iterative method for model reduction combining rational Krylov…
Magnetic resonance imaging (MRI) is known to be a slow imaging modality and undersampling in k-space has been used to increase the imaging speed. However, image reconstruction from undersampled k-space data is an ill-posed inverse problem.…
Bilevel optimization, with broad applications in machine learning, has an intricate hierarchical structure. Gradient-based methods have emerged as a common approach to large-scale bilevel problems. However, the computation of the…
Enlarged Krylov subspace methods and their s-step versions were introduced [7] in the aim of reducing communication when solving systems of linear equations Ax = b. These enlarged CG methods consist of enlarging the Krylov subspace by a…
Krylov subspace methods, such as the Conjugate Gradient (CG) and BiCGSTAB methods, are widely used in scientific computing for solving linear systems. In this study, we propose a new framework for solving large Sylvester equations in a…
Frequent Directions, as a deterministic matrix sketching technique, has been proposed for tackling low-rank approximation problems. This method has a high degree of accuracy and practicality, but experiences a lot of computational cost for…
Subspace clustering is to find underlying low-dimensional subspaces and cluster the data points correctly. In this paper, we propose a novel multi-view subspace clustering method. Most existing methods suffer from two critical issues.…
Inverse reinforcement learning (IRL) offers a powerful and general framework for learning humans' latent preferences in route recommendation, yet no approach has successfully addressed planetary-scale problems with hundreds of millions of…
We propose a fast algorithm for computing the entire ridge regression regularization path in nearly linear time. Our method constructs a basis on which the solution of ridge regression can be computed instantly for any value of the…
The "curse of dimensionality" is a well-known problem in pattern recognition. A widely used approach to tackling the problem is a group of subspace methods, where the original features are projected onto a new space. The lower dimensional…
Since being analyzed by Rokhlin, Szlam, and Tygert and popularized by Halko, Martinsson, and Tropp, randomized Simultaneous Power Iteration has become the method of choice for approximate singular value decomposition. It is more accurate…
The Rosenbrock-Krylov family of time integration schemes is an extension of Rosenbrock-W methods that employs a specific Krylov based approximation of the linear system solutions arising within each stage of the integrator. This work…
Subspace clustering is the classical problem of clustering a collection of data samples that approximately lie around several low-dimensional subspaces. The current state-of-the-art approaches for this problem are based on the…
We address the inverse problem of cosmic large-scale structure reconstruction from a Bayesian perspective. For a linear data model, a number of known and novel reconstruction schemes, which differ in terms of the underlying signal prior,…