A Powerful Truncated Newton Method for Potential Energy Minimization
A Powerful Truncated Newton Method for Potential Energy Minimization
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In our eReader you can find the full English version of the book. Read A Powerful Truncated Newton Method for Potential Energy Minimization Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book A Powerful Truncated Newton Method for Potential Energy Minimization
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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 .
What to read after A Powerful Truncated Newton Method for Potential Energy Minimization?
You can find similar books in the "Read Also" column, or choose other free books by Tamar Schlick to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
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 .
What to read after A Powerful Truncated Newton Method for Potential Energy Minimization?
You can find similar books in the "Read Also" column, or choose other free books by Tamar Schlick to read onlineMoreLess
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