Lynn M. Hubbard

Eigenvector eigenvalue theory: The diagonalization of symmetric matrices using a least-squares optimized threshold method

Abstract A least-squares threshold diagonalization algorithm is presented. The salient features of the algorithm include an internally computed series of threshold values which optimize convergence and an input parameter to simplify programmatic control of the precision of the calculated eigenvectors. The optimized threshold method is from 30 to 40 % faster than the most efficient Jacobi diagonalization routines and is roughly 20 % faster than previous threshold methods. Furthermore, the algorithm requires no allocation of additional work arrays.