ACML Version 2.0 - AMD Core Math Library for 32-bit/64-bit Linux
The ACML is a tuned math library designed for high performance on AMD64 processors including: AMD Opteron™ and AMD Athlon™ 64. 32-bit and 64-bit libraries include a full suite of Basic Linear Algebra (BLAS) routines and Linear Algebra (LAPACK) routines, plus a comprehensive suite of Fast Fourier Transforms (FFTs) in both single-, double-, single-complex and double-complex data types.
http://www.developwithamd.com/apppartnerprog/acml/home/index.cfm?action=home

ATLAS 3.5.x (optimized - Open source)
ATLAS (Automatically Tuned Linear Algebra Software). ATLAS is both a research project and a software package designed to provide portably optimal linear algebra software. The current version provides a complete BLAS API (for both C and Fortran77), and a very small subset of the LAPACK API. For all supported operations, ATLAS achieves performance on par with machine-specific tuned libraries. ATLAS can be used by anyone needing fast linear algebra routines.

GNU glibc (Open Source)
The GNU C library is used as the C library in the GNU system and most systems with the Linux kernel. The GNU C library is primarily designed to be a portable and high performance C library. GNU glibc 2.3.2 is AMD64 optimized.

GOTO Library (Open Source)
Complete BLAS Libraries (single, double, complex, double complex, levels 1, 2, and 3) for AMD Opteron processor both 32-bit and 64-bit.
These BLAS libraries contains following functions: Level 1, Level 1 extensions, Level 2, Level 3, a part of LAPACK (*laswp, *getf2, *getrf, *getrs, *gesv).

Numerical Libraries by NAG
NAG has worked closely with AMD to produce numerical libraries for the AMD64 processor architecture. The Numerical Algorithms Group specializes in the provision of numerical and statistical components to aid the solving of complex mathematical problems. Products include Numerical Libraries, Data Mining Components, Statistical and Visualization Software, Numerical Simulation, Compilers and Tools.

VGL -- graphics libraries and tools by Volume Graphics GmbH
2003 Volume Graphics offers support for the AMD64 Processor, AMD Opteron™. The 64-bit processors will play a major role in voxel graphics and image processing. Because Volume Graphics products are built on a scalable software-based processing architecture, its performance is directly linked to the underlying bandwidth of the system. 64-bit processor generations are enabling users to increase their productivity.