Reply to Comment on On the optimal symmetric purification scheme of the one-particle density matrix

Abstract

Rubensson suggested in his Comment that the 9th-order function is an optimal purification degree if one uses a Paterson-Stockmeyer method to evaluate the Holas polynomials, unlike our earlier conclusion that the 5th-order is optimal. Here we show that the Paterson-Stockmeyer factorization to evaluate the 9th-order Holas polynomial is numerically significantly less stable than the 5th-order symmetric form due to the large expansion coefficients involved. When numerical truncation is introduced as is necessary for linear scaling SCF calculations, we show that this numerical error indeed leads to a higher computational cost for the 9th-order purification as compared to the 5th-order function, leaving our previous conclusion unchanged. (C) 2012 Elsevier B.V. All rights reserved.