Conjugate gradient optimization - Revision history

Huebsch at 10:48, 6 April 2022

2022-04-06T10:48:43Z

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	[[Category:Electronic ~~Minimization]][[Category:Electronic Minimization Methods~~]][[Category:Theory]]		[[Category:Electronic minimization]][[Category:Theory]]

Karsai at 11:48, 18 March 2019

2019-03-18T11:48:42Z

← Older revision		Revision as of 11:48, 18 March 2019
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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 ~~\ref~~{~~min-en2~~}.		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\|~~Single~~ band ~~steepest descent scheme~~}}.		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}}.

Karsai: Created page with "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 success..."

2019-03-18T11:47:53Z

Created page with "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 success..."

New page

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 \ref{min-en2}.
In all following steps the preconditioned gradient <math> 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 {{TAG|Single band steepest descent scheme}}.
For further reading see {{cite|teter:prb:1989}}{{cite|bylander:prb:1990}}{{cite|press:book:1986}}.

== References ==
<references/>
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[[Category:Electronic Minimization]][[Category:Electronic Minimization Methods]][[Category:Theory]]