Acceleration of convergence in iterative methods when solving Newton-Raphson equations in second-order SCF calculations for energy-localized orbitals
✍ Scribed by Tatsuji Sano; Yasumasa J. I'Haya
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 451 KB
- Volume
- 166
- Category
- Article
- ISSN
- 0009-2614
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✦ Synopsis
Some iterative methods for solving large-scale Newton-Raphson equations in level-shifted second-order SCF calculations are tested using numerical examples for energy-localized orbitals minimizing the negative of the self-repulsion energy. In these algorithms convergence is remarkably slow by nature. It is shown that scaling of diagonal elements of a level-shifted Hessian can reduce the spectral condition number when the level-shifted Hessian has a small positive lowest eigenvalue. This simple procedure is found to maintain orthogonality of vectors and accelerate convergence significantly. The number of iterations needed in the diagonal-scaled conjugate gradient squared method is shown to be about 1 of that in the diagonal-scaled conjugate gradient or diagonal-scaled Lanczos methods.