Related papers: Performance evaluation of accelerated real and com…

The increasing number of processing elements and decreas- ing memory to core ratio in modern high-performance platforms makes efficient strong scaling a key requirement for numerical algorithms. In order to achieve efficient scalability on…

Quantum Krylov algorithms have emerged as a promising approach for ground-state energy estimation in the near-term quantum computing era. A major challenge, however, lies in their inherently substantial sampling cost, primarily due to the…

The peak performance of any SpMV depends primarily on the available memory bandwidth and its effective use. GPUs, ASICs, and new FPGAs have higher and higher bandwidth; however, for large scale and highly sparse matrices, SpMV is still a…

Sparse matrix vector multiplication (SpMV) is central to numerous data-intensive applications, but requires streaming indirect memory accesses that severely degrade both processing and memory throughput in state-of-the-art architectures.…

Krylov subspace methods are a powerful tool for efficiently solving high-dimensional linear algebra problems. In this work, we study the approximation quality that a Krylov subspace provides for estimating the numerical range of a matrix.…

We present an efficient numerical method for computing Hamiltonian matrix elements between non-orthogonal Slater determinants, focusing on the most time-consuming component of the calculation that involves a sparse array. In the usual case…

Sparse matrix-vector multiplication (SpMV) is a fundamental operation with a wide range of applications in scientific computing and artificial intelligence. However, the large scale and sparsity of sparse matrix often make it a performance…

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…

Speculative decoding and dynamic sparse attention are two complementary approaches for accelerating long-context LLM inference: the former amortizes target-model execution across multiple verifier queries, while the latter reduces each…

Fueled by its successful commercialization, the recommender system (RS) has gained widespread attention. However, as the training data fed into the RS models are often highly sensitive, it ultimately leads to severe privacy concerns,…

We suggest a technique to reduce the storage size of sparse matrices at no loss of information. We call this technique Diagonally-Adressed (DA) storage. It exploits the typically low matrix bandwidth of matrices arising in applications. For…

We describe a randomized Krylov-subspace method for estimating the spectral condition number of a real matrix A or indicating that it is numerically rank deficient. The main difficulty in estimating the condition number is the estimation of…

In this work, we propose a reduced basis method for efficient solution of parametric linear systems. The coefficient matrix is assumed to be a linear matrix-valued function that is symmetric and positive definite for admissible values of…

Sparse computations frequently appear in scientific simulations and the performance of these simulations rely heavily on the optimization of the sparse codes. The compact data structures and irregular computation patterns in sparse matrix…

Since being analyzed by Rokhlin, Szlam, and Tygert and popularized by Halko, Martinsson, and Tropp, randomized Simultaneous Power Iteration has become the method of choice for approximate singular value decomposition. It is more accurate…

A Krylov subspace recycling method for the efficient evaluation of a sequence of matrix functions acting on a set of vectors is developed. The method improves over the recycling methods presented in [Burke et al., arXiv:2209.14163, 2022] in…

This paper presents a novel framework to accelerate score-based diffusion models. It first converts the standard stable diffusion model into the Fokker-Planck formulation which results in solving large linear systems for each image. For…

This paper deals with linear algebra operations on Graphics Processing Unit (GPU) with complex number arithmetic using double precision. An analysis of their uses within iterative Krylov methods is presented to solve acoustic problems.…

Performing Bayesian inference on large spatio-temporal models requires extracting inverse elements of large sparse precision matrices for marginal variances, as well as estimating model hyperparameters. Although direct matrix factorizations…

The machine learning explosion has created a prominent trend in modern computer hardware towards low precision floating-point operations. In response, there have been growing efforts to use low and mixed precision in general scientific…