The MAGMA project aims to develop a dense linear algebra library similar to LAPACK but for heterogeneous/hybrid architectures, starting with current "Multicore+GPU" systems.
ScaLAPACK is a software package provided by Univ. of Tennessee; Univ. of California, Berkeley; Univ. of Colorado Denver; and NAG Ltd.
The GNU Scientific Library (GSL) is a numerical library for C and C++ programmers.
OpenBLAS is an optimized BLAS library based on GotoBLAS2 1.13 BSD version.
FFTW is a C subroutine library for computing the discrete Fourier transform (DFT) in one or more dimensions, of arbitrary input size, and of both real and complex data (as well as of even/odd data, i.e. the discrete cosine/sine transforms or DCT/DST).
MPICH is a high performance and widely portable implementation of the Message Passing Interface (MPI) standard.
The Open MPI Project is an open source Message Passing Interface implementation that is developed and maintained by a consortium of academic, research, and industry partners.
The Intel® oneAPI DPC++/C++Compiler provides optimizations that help your applications to run faster on Intel® 64 and IA-32 (Windows and Linux only) architectures, with support for the latest C, C++, and DPC++ language standards (including C++17).
https://www.intel.com/content/www/us/en/developer/tools/oneapi/dpc-compiler.html
The AMD Optimizing C/C++ and Fortran Compilers (“AOCC”) are a set of production compilers optimized for software performance when running on AMD host processors using the AMD “Zen” core architecture.
The NVIDIA HPC Software Development Kit (SDK) includes the proven compilers, libraries and software tools essential to maximizing developer productivity and the performance and portability of HPC applications.