An improvement of Davidson's iteration method: Applications to MRCI and MRCEPA calculations

✍ Scribed by Van Dam, H.J.J.; Van Lenthe, J.H.; Sleijpen, G.L.G.; Van Der Vorst, H.A.

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 428 KB
• Volume: 17
• Category: Article
• ISSN: 0192-8651
• DOI: 10.1002/(sici)1096-987x(199602)17:3<267::aid-jcc1>3.0.co;2-t

✦ Synopsis

Davidson's method is widely used for finding the lowest eigenvalues of large matrices. Recently, mathematicians have shown that Davidson's derivation could be improved. They have corrected the derivation yielding a new iteration method. In this article this new method is adapted for realistic MRCI and MRCEPA calculations. Results show that the new method converges sigruficantly faster in H,O and 0, with moderately elongated bonds than Davidson's original method. The new method offers new insights into the rate of convergence of Davidson's original method. 0 1996 by John Wiley & Sons, Inc. CI calculations one aims at the few lowest eigenvalues and the corresponding eigenvectors of CI Hamilton matrices. Because these matrices are large and sparse, iterative methods are the methods of choice. These methods require a matrix-vector multiplication with the CI matrix in