Nvidia presents 2M algorithm reducing complex matrix multiplication to two real GEMMs

A new paper introduces the 2M multiplication algorithm, which reduces the cost of complex matrix multiplication from three real General Matrix Multiplications (GEMMs) to just two. This approach applies to matrices with integer real and imaginary parts by utilizing quadratic time pre- and post-processing steps.

• The algorithm replaces the standard 3M method, requiring only two real GEMMs of the same size for complex inputs.
• For floating-point matrices, it integrates with the Ozaki-II scheme to achieve high performance, taking roughly twice the time of a real GEMM.
• The work also derives new algorithms for symmetric rank-k updates (SYRK/HERK) that internally use full rectangular GEMMs.

This method offers a practical, high-performance solution for computing complex floating-point GEMMs while providing corollary improvements for symmetric rank operations.