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

This paper describes modification s 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.