Large-scale simulations require efficient computation across the entire computing hierarchy. A challenge of the Exascale Computing Project (ECP) was to reconcile highly heterogeneous hardware with the myriad of applications that were required to run on ...

This paper investigates the efficient application of half-precision floating-point (FP16) arithmetic on GPUs for boosting LU decompositions in double (FP64) precision. Addressing the motivation to enhance computational efficiency, we introduce two ...

This paper presents a portable and performance-efficient approach to solve a batch of linear systems of equations using Graphics Processing Units (GPUs). Each system is represented using a special type of matrices with a band structure above and/or below ...

Vendor libraries are tuned for a specific architecture and are not portable to others. Moreover, they lack support for heterogeneity and multi-device orchestration, which is required for efficient use of contemporary HPC and cloud resources. To address ...

The sparse linear solver has become the bottleneck in a SPICE-like circuit simulator. A general sparse linear solver comprises pre-analysis, numeric factorization, and right-hand solving. The matrix ordering method in pre-analysis determines fill-...

Direct solvers for dense systems of linear equations commonly use partial pivoting to ensure numerical stability. However, pivoting can introduce significant performance overheads, such as synchronization and data movement, particularly on distributed ...

Modern GPUs equipped with mixed precision tensor core units present great potential to accelerate dense linear algebra operations such as LU factorization. However, state-of-the-art mixed half/single precision LU factorization algorithms all require the ...

LU factorization for sparse matrices is an important computing step for many engineering and scientific problems such as circuit simulation. There have been many efforts toward parallelizing and scaling this algorithm, which include the recent efforts ...

We are interested in solving linear systems arising from three applications: (1) kernel methods in machine learning, (2) discretization of boundary integral equations from mathematical physics, and (3) Schur complements formed in the factorization of ...

Many scientific applications rely on sparse direct solvers for their numerical robustness. However, performance optimization for these solvers remains a challenging task, especially on GPUs. This is due to workloads of small dense matrices that are ...

Here, the IRIS programming model is evaluated as a method to improve performance portability for heterogeneous systems that use LU matrix factorization. LU (lower-upper) factorization is considered one of the most important numerical linear ...

An augmented joint domain localized technique for computationally efficient polarimetric space–time adaptive processing (pSTAP) is proposed. In the proposed method, the signal vector to be detected is first estimated by using a modified least ...

We investigate a special class of data sparse rank-structured matrices that combine a flat block low-rank (BLR) partitioning with the use of shared (called nested in the hierarchical case) bases. This format is to $\mathcal{H}^2$ matrices what BLR is to $\...

We propose a two-parameter family of nonsymmetric dense $n\times n$ matrices $A(\alpha,\beta)$ for which LU factorization without pivoting is numerically stable, and we show how to choose $\alpha$ and $\beta$ to achieve any value of the $\infty$-norm ...

We identify a class of random, dense, $n\times n$ matrices for which LU factorization with any form of pivoting produces a growth factor typically of size at least $n/(4 \log n)$ for large $n$. The condition number of the matrices can be arbitrarily chosen, ...

Solving dense systems of linear equations is essential in applications encountered in physics, mathematics, and engineering. This paper describes our current efforts toward the development of the ADELUS package for current and next generation ...

• O ( N log 2 ⁡ N ) fast matvec and approximate LU factorization of the linear system from 2D EFIE involving open surfaces.

This paper introduces a hierarchical interpolative decomposition butterfly-LU factorization (H-IDBF-LU) preconditioner for solving two-dimensional electric-field integral equations (EFIEs) in electromagnetic scattering problems of ...

Computing units that carry out a fused multiply-add (FMA) operation with matrix arguments, referred to as tensor units by some vendors, have great potential for use in scientific computing. However, these units are inherently mixed precision, and existing ...

We parallelize the LU factorization of a hierarchical low-rank matrix ( H -matrix) on a distributed-memory computer. This is much more difficult than the H -matrix-vector multiplication due to the dataflow of the factorization, and it is much harder ...

We propose a reproducible variant of the unblocked LU factorization for graphics processor units (GPUs). For this purpose, we build upon Level-1/2 BLAS kernels that deliver correctly-rounded and reproducible results for the dot (inner) product, vector ...