Iterative diagonalization of symmetric matrices in mixed precision

TL;DR

This paper demonstrates that using mixed precision arithmetic with level-3 BLAS/LAPACK routines can significantly accelerate the diagonalization of large symmetric matrices while maintaining high accuracy, benefiting applications like electronic structure calculations.

Contribution

The authors introduce an efficient mixed precision diagonalization method that leverages 32-bit computations for speedup without sacrificing 64-bit accuracy, optimizing performance on standard hardware.

Findings

Over 30% speedup using mixed precision

Most operations performed by optimized BLAS/LAPACK routines

Potential for further improvement with problem-specific preconditioners

Abstract

Diagonalization of a large matrix is the computational bottleneck in many applications such as electronic structure calculations. We show that a speedup of over 30% can be achieved by exploiting 32-bit floating point operations, while keeping 64-bit accuracy. Moreover, most of the computationally expensive operations are performed by level-3 BLAS/LAPACK routines in our implementation, thus leading to optimal performance on most platforms. Further improvement can be made by using problem-specific preconditioners which take into account nondiagonal elements.