Squeezing the Most out of Eigenvalue Solvers on High-Performance Computers

This paper describes modifications to many of the standard algorithms used in computing eigenvalues and eigenvectors of matrices. These modifications can dramatically increase the performance of the underlying software on high-performance computers without resorting to assembler language, without significantly influencing the floating-point operation count, and without affecting the roundoff-error properties of the algorithms. The techniques are applied to a wide variety of algorithms and are beneficial in various architectural settings.