On the accuracy of the many-points local procedures

✍ Scribed by G. F. Majorino; C. Rubino

• Book ID: 104578321
• Publisher: John Wiley and Sons
• Year: 1973
• Tongue: English
• Weight: 475 KB
• Volume: 7
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/qua.560070405

✦ Synopsis

Abstract

As until now proposed in the literature, in the local energy calculations we can distinguish “few‐points” procedures, in which the number M of configurational points is strictly related to the number N of trial functions used, and statistical “many‐points” procedures, in which the number M of points can be arbitrarily increased. In this paper we demonstrate that the energy errors resulting from a “many‐points” calculation M points/N functions (M > N) can be connected in a simple way with the errors of the (^M^~N~) partial calculations N points/N functions.

This suggests a possible approach for the problem of the choice of the configurational points to be introduced in the calculation, and leads to a simple interpretation of the numerical meaning of the error associated with the ordinary Ritz energy. Numerical examples on the hydrogen atom are reported.