相关论文: Randomized LU-Householder CholeskyQR

Large-scale multi-layer networks with large numbers of nodes, edges, and layers arise across various domains, which poses a great computational challenge for the downstream analysis. In this paper, we develop an efficient randomized…

Current uncertainty quantification is memory and compute expensive, which hinders practical uptake. To counter, we develop Sketched Lanczos Uncertainty (SLU): an architecture-agnostic uncertainty score that can be applied to pre-trained…

Standard rank-revealing factorizations such as the singular value decomposition and column pivoted QR factorization are challenging to implement efficiently on a GPU. A major difficulty in this regard is the inability of standard algorithms…

Tensor-oriented multi-view subspace clustering has achieved significant strides in assessing high-order correlations and improving clustering analysis of multi-view data. Nevertheless, most of existing investigations are typically hampered…

We propose a novel randomized framework for the estimation problem of large-scale linear statistical models, namely Sequential Least-Squares Estimators with Fast Randomized Sketching (SLSE-FRS), which integrates Sketch-and-Solve and…

Matrices with off-diagonal decay appear in a variety of fields in mathematics and in numerous applications, such as signal processing, statistics, communications engineering, condensed matter physics, and quantum chemistry. Numerical…

As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in order to take advantage of the architectural features on these…

In this article, square-root formulations of the statistical linear regression filter and smoother are developed. Crucially, the method uses QR decompositions rather than Cholesky downdates. This makes the method inherently more numerically…

The maximum correntropy criterion (MCC) methodology is recognized to be a robust filtering strategy with respect to outliers and shown to outperform the classical Kalman filter (KF) for estimation accuracy in the presence of non-Gaussian…

This article explores and analyzes the unsupervised clustering of large partially observed graphs. We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model. The clustering is…

We consider the computation of roots of polynomials expressed in the Chebyshev basis. We extend the QR iteration presented in [Eidelman, Y., Gemignani, L., and Gohberg, I., Numer. Algorithms, 47.3 (2008): pp. 253-273] introducing an…

The classic rank-revealing QR factorization factorizes a matrix $A$ as $AP=QR$ where $P$ permutes the columns of $A$, $Q$ is an orthogonal matrix, and $R$ is upper triangular with non-increasing diagonal entries. This is called…

Newton systems in quadratic programming (QP) methods are often solved using direct Cholesky or LDL factorizations. When the linear systems in successive iterations differ by a low-rank modification (as is common in active set and augmented…

We classify a family of matrices of shift operators that can be factorised in a computationally tractable manner with the Cholesky algorithm. Such matrices arise in the linear quadratic regulator problem, and related areas. We use the…

Interpolative and CUR decompositions involve "natural bases" of row and column subsets, or skeletons, of a given matrix that approximately span its row and column spaces. These low-rank decompositions preserve properties such as sparsity or…

Integral equations are commonly encountered when solving complex physical problems. Their discretization leads to a dense kernel matrix that is block or hierarchically low-rank. This paper proposes a new way to build a low-rank…

We present a fast direct algorithm for computing symmetric factorizations, i.e. $A = WW^T$, of symmetric positive-definite hierarchical matrices with weak-admissibility conditions. The computational cost for the symmetric factorization…

Kernel-based clustering algorithm can identify and capture the non-linear structure in datasets, and thereby it can achieve better performance than linear clustering. However, computing and storing the entire kernel matrix occupy so large…

Randomized sampling has recently been proven a highly efficient technique for computing approximate factorizations of matrices that have low numerical rank. This paper describes an extension of such techniques to a wider class of matrices…

For large-scale discrete ill-posed problems, LSQR, a Lanczos bidiagonalization process based Krylov method, is most often used. It is well known that LSQR has natural regularizing properties, where the number of iterations plays the role of…