Conjugate gradient optimization: Difference between revisions
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expectation value of the Hamiltonian using a successive number of | expectation value of the Hamiltonian using a successive number of | ||
conjugate gradient steps. | conjugate gradient steps. | ||
The first step is equal to the steepest descent step in section | The first step is equal to the steepest descent step in section {{TAG|Single band steepest descent scheme}}. | ||
In all following steps the preconditioned gradient <math> g^N_{n} </math> | In all following steps the preconditioned gradient <math> g^N_{n} </math> | ||
is conjugated to the previous search direction. | is conjugated to the previous search direction. | ||
The resulting conjugate gradient algorithm is almost as efficient as the algorithm | The resulting conjugate gradient algorithm is almost as efficient as the algorithm | ||
given in {{TAG| | given in {{TAG|Efficient single band eigenvalue-minimization}}. | ||
For further reading see {{cite|teter:prb:1989}}{{cite|bylander:prb:1990}}{{cite|press:book:1986}}. | For further reading see {{cite|teter:prb:1989}}{{cite|bylander:prb:1990}}{{cite|press:book:1986}}. | ||
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<references/> | <references/> | ||
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[[Category:Electronic | [[Category:Electronic minimization]][[Category:Theory]] | ||
Latest revision as of 10:48, 6 April 2022
Instead of the previous iteration scheme, which is just some kind of Quasi-Newton scheme, it also possible to optimize the expectation value of the Hamiltonian using a successive number of conjugate gradient steps. The first step is equal to the steepest descent step in section Single band steepest descent scheme. In all following steps the preconditioned gradient [math]\displaystyle{ g^N_{n} }[/math] is conjugated to the previous search direction. The resulting conjugate gradient algorithm is almost as efficient as the algorithm given in Efficient single band eigenvalue-minimization. For further reading see [1][2][3].