Related papers: Solving sparse linear systems with approximate inv…
A parallelization of a sweeping preconditioner for 3D Helmholtz equations without large cavities is introduced and benchmarked for several challenging velocity models. The setup and application costs of the sequential preconditioner are…
Scaling up hardware systems has become an important tactic for improving performance as Moore's law fades. Unfortunately, simulations of large hardware systems are often a design bottleneck due to slow throughput and long build times. In…
Sparse matrix ordering is a vital optimization technique often employed for solving large-scale sparse matrices. Its goal is to minimize the matrix bandwidth by reorganizing its rows and columns, thus enhancing efficiency. Conventional…
In recent years, hardware implementations of Ising machines have emerged as a viable alternative to quantum computing for solving hard optimization problems among other applications. Unlike quantum hardware, dense connectivity can be…
In this paper, we propose a general framework that transforms the problems of designing sparse finite-impulseresponse linear equalizers and non-linear decision-feedback equalizers, for multiple antenna systems, into the problem of…
Fast computation of demagnetization curves is essential for the computational design of soft magnetic sensors or permanent magnet materials. We show that a sparse preconditioner for a nonlinear conjugate gradient energy minimizer can lead…
Solving sparse systems of linear equations is a fundamental problem in the field of numerical methods, with applications spanning from circuit design to urban planning. These problems can have millions of constraints, such as when laying…
Tensor accelerators have gained popularity because they provide a cheap and efficient solution for speeding up computational-expensive tasks in Deep Learning and, more recently, in other Scientific Computing applications. However, since…
The matrices used in many computational settings are naturally sparse, holding a small percentage of nonzero elements. Storing such matrices in specialized sparse formats enables algorithms that avoid wasting computation on zeros,…
Automated code generation and performance enhancements for sparse tensor algebra have become essential in many real-world applications, such as quantum computing, physical simulations, computational chemistry, and machine learning. General…
We introduce a parallel algorithm to construct a preconditioner for solving a large, sparse linear system where the coefficient matrix is a Laplacian matrix (a.k.a., graph Laplacian). Such a linear system arises from applications such as…
Sparse compiler is a promising solution for sparse tensor algebra optimization. In compiler implementation, reduction in sparse-dense hybrid algebra plays a key role in performance. Though GPU provides various reduction semantics that can…
We present a robust and scalable preconditioner for the solution of large-scale linear systems that arise from the discretization of elliptic PDEs amenable to rank compression. The preconditioner is based on hierarchical low-rank…
A primary computational problem in kernel regression is solution of a dense linear system with the $N\times N$ kernel matrix. Because a direct solution has an O($N^3$) cost, iterative Krylov methods are often used with fast matrix-vector…
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…
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…
Packing and covering semidefinite programs (SDPs) appear in natural relaxations of many combinatorial optimization problems as well as a number of other applications. Recently, several techniques were proposed, that utilize the particular…
We give a new theoretical tool to solve sparse systems with finitely many solutions. It is based on toric varieties and basic linear algebra; eigenvalues, eigenvectors and coefficient matrices. We adapt Eigenvalue theorem and Eigenvector…
We describe a parallel solver for the discretized weakly singular space-time boundary integral equation of the spatially two-dimensional heat equation. The global space-time nature of the system matrices leads to improved parallel…
Large language models (LLMs) have demonstrated exceptional proficiency in understanding and generating human language, but efficient inference on resource-constrained embedded devices remains challenging due to large model sizes and…