A Powerful Truncated Newton Method for Potential Energy Minimization

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A Powerful Truncated Newton Method for Potential Energy Minimization
Tamar Schlick
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Clearly, without preconditioning (TN-A), round-off occurs in CG and many iterations are performed. In this first version, almost all CG loops terminate by exceeding the allowable number of iterations, and not by satisfying the truncated Newton criterion. With diagonal preconditioning (TN-B), almost as many CG iterations are performed, but the truncated criterion is satisfied.
Tremendous improvement is realized with the preconditioner XI k (TN-C). The truncation criterion is now satisfied in a f
...raction of the number of CG iterations performed in the previous two versions, typically 9 iterations. The cumulative number of inner loop iterations for this version is 137. About 1/6 of the number required for the 2 variants above ! This demonstrates not only the necessity and power of preconditioning in Conjugate Gradient methods but also the effectiveness of the present preconditioning matrix.
The performance of the truncated Newton version with the finite-difference approximation to HA (TN-D) is described for h = 1CT 4 .


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