Related papers: Linear Complexity $\mathcal{H}^2$ Direct Solver fo…
Mixed-integer programming (MIP) extends linear programming by incorporating both continuous and integer decision variables, making it widely used in production planning, logistics scheduling, and resource allocation. However, MIP remains…
The current computer architecture has moved towards the multi/many-core structure. However, the algorithms in the current sequential dense numerical linear algebra libraries (e.g. LAPACK) do not parallelize well on multi/many-core…
Sequential computation is well understood but does not scale well with current technology. Within the next decade, systems will contain large numbers of processors with potentially thousands of processors per chip. Despite this, many…
A new generation of manycore processors is on the rise that offers dozens and more cores on a chip and, in a sense, fuses host processor and accelerator. In this paper we target the efficient training of generalized linear models on these…
Multi-level numerical methods that obtain the exact solution of a linear system are presented. The methods are devised by combining ideas from the full multi-grid algorithm and perfect reconstruction filters. The problem is stated as…
High-throughput neural network inference requires coordinating many optimization decisions, including parallel tiling, microkernel selection, and data layout. The product of these decisions forms a search space of programs which is…
We present a parallel computing strategy for a hybridizable discontinuous Galerkin (HDG) nested geometric multigrid (GMG) solver. Parallel GMG solvers require a combination of coarse-grain and fine-grain parallelism to improve time to…
Problems from graph drawing, spectral clustering, network flow and graph partitioning can all be expressed in terms of graph Laplacian matrices. There are a variety of practical approaches to solving these problems in serial. However, as…
Nucleus decompositions have been shown to be a useful tool for finding dense subgraphs. The coreness value of a clique represents its density based on the number of other cliques it is adjacent to. One useful output of nucleus decomposition…
This paper introduces the hierarchical interpolative factorization for integral equations (HIF-IE) associated with elliptic problems in two and three dimensions. This factorization takes the form of an approximate generalized LU…
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…
We parallelize density-matrix renormalization group to directly extend it to 2-dimensional ($n$-leg) quantum lattice models. The parallelization is made mainly on the exact diagonalization for the superblock Hamiltonian since the part…
The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…
We formally introduce a systematic (de/re)-composition approach, based on the algebraic formalism of "Multi-Dimensional Homomorphisms (MDHs)". Our approach is designed as general enough to be applicable to a wide range of data-parallel…
In this work, we propose an adaptive geometric multigrid method for the solution of large-scale finite cell flow problems. The finite cell method seeks to circumvent the need for a boundary-conforming mesh through the embedding of the…
Direct factorization methods for the solution of large, sparse linear systems that arise from PDE discretizations are robust, but typically show poor time and memory scalability for large systems. In this paper, we describe an efficient…
This paper introduces sTiles, a GPU-accelerated framework for factorizing sparse structured symmetric matrices. By leveraging tile algorithms for fine-grained computations, sTiles uses a structure-aware task execution flow to handle…
While deep learning excels in natural image and language processing, its application to high-dimensional data faces computational challenges due to the dimensionality curse. Current large-scale data tools focus on business-oriented…
The hierarchical interpolative factorization (HIF) offers an efficient way for solving or preconditioning elliptic partial differential equations. By exploiting locality and low-rank properties of the operators, the HIF achieves…
Generalized sparse matrix-matrix multiplication is a key primitive for many high performance graph algorithms as well as some linear solvers such as multigrid. We present the first parallel algorithms that achieve increasing speedups for an…