What is the best matrix multiplication algorithm?

Question

What is the best matrix multiplication algorithm? What means 'the best'for me? It means the fastest and ready for todays machines.

Please give links to pseudocode if you can.

Answer 1

BLAS is the best ready-to-use efficient matrix multiplication library. There are many different implementation. Here is a benchmark I made for some implementations on a MacBook Pro with dual-core Intel Core 2 Duo 2.66 GHz :

• gotoBLAS2 (open-source) : https://www.tacc.utexas.edu/research-development/tacc-software/gotoblas2
• ATLAS (open-source) : http://math-atlas.sourceforge.net/
• Accelerate.framework (Apple) : http://developer.apple.com/performance/accelerateframework.html
• a non-optimized, but portable, implementation that I called 'vanilla' (from the GSL)

There are also other commercial implementations that I didn't test here :

• MKL (Intel) : http://software.intel.com/en-us/articles/intel-mkl/
• ACML (AMD) : http://developer.amd.com/cpu/Libraries/acml/Pages/default.aspx