MUMPS (MUltifrontal Massively Parallel sparse direct Solver) solves a sparse system of linear equations A x = b using Gaussian elimination.

AIGER is a format, library and set of utilities for AIGs. The focus is on conversion utilities and a generic reader and writer API.

HiGHS provides serial and parallel solvers for large-scale sparse linear programming (LP), mixed-integer programming (MIP), and quadratic programming (QP) models

PETSc, pronounced PET-see (the S is silent), is a suite of data structures and routines for the scalable (parallel) solution of scientific applications modeled by partial differential equations.

CHOLMOD is a set of routines for factorizing sparse symmetrix positive definite matrices, updating/downdating sparse Cholesky factorizations and other related operations.

Armadillo is a C++ linear algebra library, aiming towards a good balance between speed and ease of use. It is useful for algorithm development directly in C++, or quick conversion of research code into production environments. It can be used for machine learning, pattern recognition, signal processing, bioinformatics, statistics, econometrics, etc. The library provides efficient classes for vectors, matrices and cubes, as well as 150+ associated functions (e.g., contiguous and non-contiguous submatrix views).

The p4est software library enables the dynamic management of a collection of adaptive octrees, conveniently called a forest of octrees. p4est is designed to work in parallel and scales to hundreds of thousands of processor cores.

SCOTCH is a set of programs and libraries which implement the static mapping and sparse matrix reordering algorithms developed within the SCOTCH project. Its purpose is to apply graph theory, with a divide and conquer approach, to scientific computing problems such as graph and mesh partitioning, static mapping, and sparse matrix ordering, in application domains ranging from structural mechanics to operating systems or bio-chemistry.

Matio is a library for reading and writing MAT files. It supports compressed MAT files, as well as newer (version 7.3) MAT files.

Bitwuzla is a SMT solver for the theories of fixed-size bit-vectors, floating-point arithmetic, arrays, uninterpreted functions and their combinations.

UMFPACK is a set of routines for solving unsymmetric sparse linear systems using the Unsymmetric MultiFrontal method and direct sparse LU factorization.

The GNU Scientific Library is a library for numerical analysis in C and C++. It includes a wide range of mathematical routines, with over 1000 functions in total. Subject areas covered by the library include: differential equations, linear algebra, Fast Fourier Transforms and random numbers.

HighFive is a header-only C++11 friendly interface for libhdf5. It supports STL vector/string, Boost::UBLAS, Boost::Multi-array and Xtensor; and handles C++ from/to HDF5 with automatic type mapping. HighFive does not require additional libraries.

The dune-functions module provides an abstraction layer for global finite element functions. Its two main concepts are functions implemented as callable objects, and bases of finite element spaces.

This DUNE module provides interface and implementation for shape functions defined on the DUNE reference elements. In addition to the shape function, interpolation operators and special keys are provided which can be used to assemble global function spaces on finite-element grids.

This package provides an interface and implementation for shape functions defined on the DUNE reference elements. In addition to the shape function, interpolation operators and special keys are provided which can be used to assemble global function spaces on finite-element grids.

Openspecfun provides AMOS and Faddeeva. AMOS (from Netlib) is a portable package for Bessel Functions of a Complex Argument and Nonnegative Order; it contains subroutines for computing Bessel functions and Airy functions. Faddeeva allows computing the various error functions of arbitrary complex arguments (Faddeeva function, error function, complementary error function, scaled complementary error function, imaginary error function, and Dawson function); given these, one can also easily compute Voigt functions, Fresnel integrals, and similar related functions as well.

SLEEF (SIMD Library for Evaluating Elementary Functions) is a library that implements vectorized versions of all C99 real floating point math functions. It can utilize SIMD instructions that are available on modern processors.

GKlib is a library of various helper routines and frameworks used by software from KarypisLab, such as METIS.

CCOLAMD is library for computing a permutation vector for a matrix with which the LU factorization becomes sparser. It is a variant of COLAMD which has the the option to apply constraints to the ordering.

NOMAD is a C++ implementation of the mesh-adaptive direct search (MADS) algorithm, designed for difficult blackbox optimization problems. These problems occur when the functions defining the objective and constraints are the result of costly computer simulations.

Mongoose is a library for graph partitioning by computing edge cuts using a coarsening and refinement framework.

The SPQR (SuiteSparseQR) package provides sparse QR factorization based on the multifrontal method, using BLAS for the frontal matrices.

MUMPS (MUltifrontal Massively Parallel sparse direct Solver) solves a sparse system of linear equations A x = b using Gaussian elimination.

SUNDIALS is a family of software packages implemented with the goal of providing robust time integrators and nonlinear solvers that can easily be incorporated into existing simulation codes.