Related papers: Supercomputer Environment for Recursive Matrix Alg…

The solution of a sparse system of linear equations is ubiquitous in scientific applications. Iterative methods, such as the Preconditioned Conjugate Gradient method (PCG), are normally chosen over direct methods due to memory and…

This paper introduces RankMap, a platform-aware end-to-end framework for efficient execution of a broad class of iterative learning algorithms for massive and dense datasets. Our framework exploits data structure to factorize it into an…

A parallel algorithm for the implementation of the recursive Green's function technique, which is extensively applied in the coherent scattering formalism, is developed. The algorithm performs a domain decomposition of the scattering region…

Coreset, which is a summary of the original dataset in the form of a small weighted set in the same sample space, provides a promising approach to enable machine learning over distributed data. Although viewed as a proxy of the original…

Block encoding of sparse matrices underpins powerful quantum algorithms such as quantum singular value transformation, Hamiltonian simulation, and quantum linear solvers, yet its efficient gate-level realization for general sparse matrices…

Circulant matrices are an important family of operators, which have a wide range of applications in science and engineering related fields. They are in general non-sparse and non-unitary. In this paper, we present efficient quantum circuits…

Generalized sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. Here we show that SpGEMM also yields efficient…

In-memory computing technology is used extensively in artificial intelligence devices due to lower power consumption and fast calculation of matrix-based functions. The development of such a device and its integration in a system takes a…

We consider the least-squares approximation of a matrix C in the set of doubly stochastic matrices with the same sparsity pattern as C. Our approach is based on applying the well-known Alternating Direction Method of Multipliers (ADMM) to a…

While several numerical techniques are available for predicting the dynamics of non-Markovian open quantum systems, most struggle with simulations for very long memory and propagation times, e.g., due to superlinear scaling with the number…

We present a general class of compressed sensing matrices which are then demonstrated to have associated sublinear-time sparse approximation algorithms. We then develop methods for constructing specialized matrices from this class which are…

Hashing method maps similar data to binary hashcodes with smaller hamming distance, and it has received a broad attention due to its low storage cost and fast retrieval speed. However, the existing limitations make the present algorithms…

The LINPACK benchmark reports the performance of a computer for solving a system of linear equations with dense random matrices. Although this task was not designed with a real application directly in mind, the LINPACK benchmark has been…

In the realm of computer systems, efficient utilisation of the CPU (Central Processing Unit) has always been a paramount concern. Researchers and engineers have long sought ways to optimise process execution on the CPU, leading to the…

In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…

In this paper, a new method is proposed for sparse PCA based on the recursive divide-and-conquer methodology. The main idea is to separate the original sparse PCA problem into a series of much simpler sub-problems, each having a closed-form…

While quantum algorithms for solving large scale systems of linear equations offer potentially exponential speedups, their application has largely been confined to sparse matrices. This work extends the scope of these algorithms to a broad…

Sparse matrix representations are ubiquitous in computational science and machine learning, leading to significant reductions in compute time, in comparison to dense representation, for problems that have local connectivity. The adoption of…

This paper highlights new opportunities for designing large-scale machine learning systems as a consequence of blurring traditional boundaries that have allowed algorithm designers and application-level practitioners to stay -- for the most…

To respond to the need of efficient training and inference of deep neural networks, a plethora of domain-specific hardware architectures have been introduced, such as Google Tensor Processing Units and NVIDIA Tensor Cores. A common feature…