相关论文: An Efficient Algorithm For Simulating Fracture Usi…
This paper presents a novel implicit scheme for the constraint resolution in real-time finite element simulations in the presence of contact and friction. Instead of using the standard motion correction scheme, we propose an iterative…
This paper proposes an effective low-rank alternating direction doubling algorithm (R-ADDA) for computing numerical low-rank solutions to large-scale sparse continuous-time algebraic Riccati matrix equations. The method is based on the…
This paper presents a new algorithmic framework for computing sparse solutions to large-scale linear discrete ill-posed problems. The approach is motivated by recent perspectives on iteratively reweighted norm schemes, viewed through the…
We propose a variant of the Frank-Wolfe algorithm for solving a class of sparse/low-rank optimization problems. Our formulation includes Elastic Net, regularized SVMs and phase retrieval as special cases. The proposed Primal-Dual Block…
We study numerical integration of smooth functions defined over the $s$-dimensional unit cube. A recent work by Dick et al. (2019) has introduced so-called extrapolated polynomial lattice rules, which achieve the almost optimal rate of…
Structured low-rank (SLR) algorithms, which exploit annihilation relations between the Fourier samples of a signal resulting from different properties, is a powerful image reconstruction framework in several applications. This scheme relies…
Estimation of the precision matrix (or inverse covariance matrix) is of great importance in statistical data analysis and machine learning. However, as the number of parameters scales quadratically with the dimension $p$, computation…
Matrix factorization (MF) is a widely used collaborative filtering (CF) algorithm for recommendation systems (RSs), due to its high prediction accuracy, great flexibility and high efficiency in big data processing. However, with the…
Recovery of low-rank matrices has recently seen significant activity in many areas of science and engineering, motivated by recent theoretical results for exact reconstruction guarantees and interesting practical applications. A number of…
In this work, we examine a numerical phase-field fracture framework in which the crack irreversibility constraint is treated with a primal-dual active set method and a linearization is used in the degradation function to enhance the…
We describe spatio-temporal random processes using linear mixed models. We show how many commonly used models can be viewed as special cases of this general framework and pay close attention to models with separable or product-sum…
The minimum degree algorithm is one of the most widely-used heuristics for reducing the cost of solving large sparse systems of linear equations. It has been studied for nearly half a century and has a rich history of bridging techniques…
Numerous practical medical problems often involve data that possess a combination of both sparse and non-sparse structures. Traditional penalized regularizations techniques, primarily designed for promoting sparsity, are inadequate to…
The Cholesky decomposition plays an important role in finding the inverse of the correlation matrices. As it is a fast and numerically stable for linear system solving, inversion, and factorization compared to singular valued decomposition…
We analyze a distributed algorithm to compute a low-rank matrix factorization on $N$ clients, each holding a local dataset $\mathbf{S}^i \in \mathbb{R}^{n_i \times d}$, mathematically, we seek to solve $min_{\mathbf{U}^i \in…
Estimating covariance parameters for multivariate spatial Gaussian random fields is computationally challenging, as the number of parameters grows rapidly with the number of variables, and likelihood evaluation requires operations of order…
The efficient and accurate QR decomposition for matrices with hierarchical low-rank structures, such as HODLR and hierarchical matrices, has been challenging. Existing structure-exploiting algorithms are prone to numerical instability as…
This paper describes a direct solver algorithm for a sequence of finite element meshes that are h-refined towards one or several point singularities. For such a sequence of grids, the solver delivers linear computational cost O(N) in terms…
In this paper, we study an efficient algorithm for constructing point sets underlying quasi-Monte Carlo integration rules for weighted Korobov classes. The algorithm presented is a reduced fast component-by-component digit-by-digit…
The state-of-the-art online learning models generally conduct a single online gradient descent when a new sample arrives and thus suffer from suboptimal model weights. To this end, we introduce an online broad learning system framework with…