Related papers: Serinv: A Scalable Library for the Selected Invers…

Selected inversion is essential for applications such as Bayesian inference, electronic structure calculations, and inverse covariance estimation, where computing only specific elements of large sparse matrix inverses significantly reduces…

We describe an efficient parallel implementation of the selected inversion algorithm for distributed memory computer systems, which we call \texttt{PSelInv}. The \texttt{PSelInv} method computes selected elements of a general sparse matrix…

This paper generalizes the parallel selected inversion algorithm called PSelInv to sparse non- symmetric matrices. We assume a general sparse matrix A has been decomposed as PAQ = LU on a distributed memory parallel machine, where L, U are…

Block matrix structure is commonly arising is various physics and engineering applications. There are various advantages in preserving the blocks structure while computing the inversion of such partitioned matrices. In this context, using…

We develop a method for improving the parallel scalability of the recently developed parallel selected inversion algorithm [Jacquelin, Lin and Yang 2014], named PSelInv, on massively parallel distributed memory machines. In the PSelInv…

This paper presents an architecture-friendly k-means clustering algorithm called SIVF for a large-scale and high-dimensional sparse data set. Algorithm efficiency on time is often measured by the number of costly operations such as…

Gradient descent optimizations and backpropagation are the most common methods for training neural networks, but they are computationally expensive for real time applications, need high memory resources, and are difficult to converge for…

Block projections have been used, in [Eberly et al. 2006], to obtain an efficient algorithm to find solutions for sparse systems of linear equations. A bound of softO(n^(2.5)) machine operations is obtained assuming that the input matrix…

Sparse matrix-vector multiplication (SpMV) is a central building block for scientific software and graph applications. Recently, heterogeneous processors composed of different types of cores attracted much attention because of their…

How can we compute the pseudoinverse of a sparse feature matrix efficiently and accurately for solving optimization problems? A pseudoinverse is a generalization of a matrix inverse, which has been extensively utilized as a fundamental…

Sparse Triangular Solve (SpTRSV) is an important computational kernel used in the solution of sparse linear algebra systems in many scientific and engineering applications. It is diffcult to parallelize SpTRSV in today's architectures. The…

We introduce an algorithm for efficiently representing convolution with zero-padding and stride as a sparse transformation matrix, applied to a vectorized input through sparse matrix-vector multiplication (SpMV). We provide a theoretical…

Block-sparse regularization is already well-known in active thermal imaging and is used for multiple measurement based inverse problems. The main bottleneck of this method is the choice of regularization parameters which differs for each…

Sparse matrices and linear algebra are at the heart of scientific simulations. More than 70 sparse matrix storage formats have been developed over the years, targeting a wide range of hardware architectures and matrix types. Each format is…

The inversion of extremely high order matrices has been a challenging task because of the limited processing and memory capacity of conventional computers. In a scenario in which the data does not fit in memory, it is worth to consider…

Sparse convolution plays a pivotal role in emerging workloads, including point cloud processing in AR/VR, autonomous driving, and graph understanding in recommendation systems. Since the computation pattern is sparse and irregular,…

Conventional deep convolutional neural networks (CNNs) apply convolution operators uniformly in space across all feature maps for hundreds of layers - this incurs a high computational cost for real-time applications. For many problems such…

Deep neural networks employ specialized architectures for vision, sequential and language tasks, yet this proliferation obscures their underlying commonalities. We introduce a unified matrix-order framework that casts convolutional,…

The multiplication of a sparse matrix with a dense vector (SpMV) is a key component in many numerical schemes and its performance is known to be severely limited by main memory access. Several numerical schemes require the multiplication of…

The algorithms in the current sequential numerical linear algebra libraries (e.g. LAPACK) do not parallelize well on multicore architectures. A new family of algorithms, the tile algorithms, has recently been introduced. Previous research…