相关论文: $O(N)$ distributed direct factorization of structu…

We present new algorithms for the randomized construction of hierarchically semi-separable matrices, addressing several practical issues. The HSS construction algorithms use a partially matrix-free, adaptive randomized projection scheme to…

Neural networks are often challenging to work with due to their large size and complexity. To address this, various methods aim to reduce model size by sparsifying or decomposing weight matrices, such as magnitude pruning and low-rank or…

We present a technique for significantly speeding up Alternating Least Squares (ALS) and Gradient Descent (GD), two widely used algorithms for tensor factorization. By exploiting properties of the Khatri-Rao product, we show how to…

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…

We introduce Sparse-HFS, a scalable algorithm that can compute solutions to SSL problems using only O(n polylog(n)) space and O(m polylog(n)) time.

Motivated by the development of computer theory, the sorting algorithm is emerging in an endless stream. Inspired by decrease and conquer method, we propose a brand new sorting algorithmUltimately Heapsort. The algorithm consists of two…

The parallel linear equations solver capable of effectively using 1000+ processors becomes the bottleneck of large-scale implicit engineering simulations. In this paper, we present a new hierarchical parallel master-slave-structural…

With the aggressive scaling of VLSI technology, the explosion of layout patterns creates a critical bottleneck for DFM applications like OPC. Pattern clustering is essential to reduce data complexity, yet existing methods struggle with…

Efficient task scheduling is paramount in parallel programming on multi-core architectures, where tasks are fundamental computational units. QR factorization is a critical sub-routine in Sequential Least Squares Quadratic Programming…

Graph partitioning schedules parallel calculations like sparse matrix-vector multiply (SpMV). We consider contiguous partitions, where the $m$ rows (or columns) of a sparse matrix with $N$ nonzeros are split into $K$ parts without…

We present a new algorithm for finding a near optimal low-rank approximation of a matrix $A$ in $O(nnz(A))$ time. Our method is based on a recursive sampling scheme for computing a representative subset of $A$'s columns, which is then used…

We present a fast and approximate multifrontal solver for large-scale sparse linear systems arising from finite-difference, finite-volume or finite-element discretization of high-frequency wave equations. The proposed solver leverages the…

Efficient solutions of large-scale, ill-conditioned and indefinite algebraic equations are ubiquitously needed in numerous computational fields, including multiphysics simulations, machine learning, and data science. Because of their…

In this paper, we tackle two important problems in low-rank learning, which are partial singular value decomposition and numerical rank estimation of huge matrices. By using the concepts of Krylov subspaces such as Golub-Kahan…

We present a parallel algorithm for computing the approximate factorization of an $N$-by-$N$ kernel matrix. Once this factorization has been constructed (with $N \log^2 N $ work), we can solve linear systems with this matrix with $N \log N…

In high dimensional regression, feature clustering by their effects on outcomes is often as important as feature selection. For that purpose, clustered Lasso and octagonal shrinkage and clustering algorithm for regression (OSCAR) are used…

Hierarchical matrices can be used to construct efficient preconditioners for partial differential and integral equations by taking advantage of low-rank structures in triangular factorizations and inverses of the corresponding stiffness…

Sparse regularization techniques are well-established in machine learning, yet their application in neural networks remains challenging due to the non-differentiability of penalties like the $L_1$ norm, which is incompatible with stochastic…

Incomplete factorization is a powerful preconditioner for Krylov subspace methods for solving large-scale sparse linear systems. Existing incomplete factorization techniques, including incomplete Cholesky and incomplete LU factorizations,…

We study the Sparse Plus Low-Rank decomposition problem (SLR), which is the problem of decomposing a corrupted data matrix into a sparse matrix of perturbations plus a low-rank matrix containing the ground truth. SLR is a fundamental…