Related papers: Hierarchical Precision and Recursion for Accelerat…
Hierarchical matrix approximations have gained significant traction in the machine learning and scientific community as they exploit available low-rank structures in kernel methods to compress the kernel matrix. The resulting compressed…
Many important real-world applications, such as System Identification with Gaussian Processes, involve solving linear systems with symmetric positive-definite matrices. The iterative CG method and direct solvers based on the Cholesky…
This paper presents a performant and portable recursive implementation of triangular matrix-matrix multiplication (TRMM) and triangular solve (TRSM) in Julia for GPUs, two kernels that underlie many linear-algebra algorithms. We restructure…
Real-time, energy-efficient inference on edge devices is essential for graph classification across a range of applications. Hyperdimensional Computing (HDC) is a brain-inspired computing paradigm that encodes input features into…
With the emergence of mixed precision capabilities in hardware, iterative refinement schemes for solving linear systems $Ax=b$ have recently been revisited and reanalyzed in the context of three or more precisions. These new analyses show…
With the hardware support for half-precision arithmetic on NVIDIA V100 GPUs, high-performance computing applications can benefit from lower precision at appropriate spots to speed up the overall execution time. In this paper, we investigate…
Solving large dense linear systems and eigenvalue problems is a core requirement in many areas of scientific computing, but scaling these operations beyond a single GPU remains challenging within modern programming frameworks. While highly…
Support for lower precision computation is becoming more common in accelerator hardware due to lower power usage, reduced data movement and increased computational performance. However, computational science and engineering (CSE) problems…
Incomplete factorization is a widely used preconditioning technique for Krylov subspace methods for solving large-scale sparse linear systems. Its multilevel variants, such as ILUPACK, are more robust for many symmetric or unsymmetric…
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…
This paper presents a GPU-accelerated framework for solving block tridiagonal linear systems that arise naturally in numerous real-time applications across engineering and scientific computing. Through a multi-stage permutation strategy…
I present HPRMAT, a high-performance solver library for the linear systems arising in R-matrix coupled-channel scattering calculations in nuclear physics. Designed as a drop-in replacement for the linear algebra routines in existing…
Tile low rank representations of dense matrices partition them into blocks of roughly uniform size, where each off-diagonal tile is compressed and stored as its own low rank factorization. They offer an attractive representation for many…
This article introduces HYLU, a hybrid parallel LU factorization-based general-purpose solver designed for efficiently solving sparse linear systems (Ax=b) on multi-core shared-memory architectures. The key technical feature of HYLU is the…
Matrix-multiplication units (MXUs) are now prevalent in every computing platform. The key attribute that makes MXUs so successful is the semiring structure, which allows tiling for both parallelism and data reuse. Nonetheless,…
Driven by the insatiable needs to process ever larger amount of data with more complex models, modern computer processors and accelerators are beginning to offer half precision floating point arithmetic support, and extremely optimized…
Support for lower precision computation is becoming more common in accelerator hardware due to lower power usage, reduced data movement and increased computational performance. However, computational science and engineering (CSE) problems…
Cholesky linear solvers are a critical bottleneck in challenging applications within computer graphics and scientific computing. These applications include but are not limited to elastodynamic barrier methods such as Incremental Potential…
Gaussian processes (GPs) are a widely used regression tool, but the cubic complexity of exact solvers limits their scalability. To address this challenge, we extend the GPRat library by incorporating a fully GPU-resident GP prediction…
Solving sparse linear systems from discretized PDEs is challenging. Direct solvers have in many cases quadratic complexity (depending on geometry), while iterative solvers require problem dependent preconditioners to be robust and…