Indecomposable module - Revision history

en>AxelBoldt: /* Examples */ +Pruefer group

2014-12-07T17:24:45Z

Examples: +Pruefer group

← Older revision		Revision as of 19:24, 7 December 2014
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	~~'''DIIS''' ('''direct inversion in the iterative subspace''' or '''direct inversion~~ of the ~~iterative subspace''')~~, ~~also known as '''Pulay mixing'''~~, ~~is an [[extrapolation]] technique~~. ~~DIIS was developed by [[Peter Pulay]] in the field of computational [[quantum chemistry]]~~ with ~~the intent to accelerate and stabilize the convergence~~ of ~~the [[Hartree–Fock]] self-consistent field method~~.~~<ref>{{cite journal\|last=Pulay\|first=Péter \|year=1980\|title=Convergence acceleration~~ of ~~iterative sequences~~. the ~~case~~ of ~~SCF iteration\|journal=Chemical Physics Letters\|volume=73\|issue=2\|pages=393–398\|doi=10~~.~~1016/0009-2614(80)80396-4}}~~<~~/ref~~><ref>{{cite journal\|last=Pulay\|first=Péter \|year=1982\|title=Improved SCF Convergence Acceleration\|journal=Journal of Computational Chemistry\|volume=3\|issue=4\|pages=556–560\|doi=10.1002/jcc.540030413}}</ref>		Succeeding with a home-based business takes a lot of time, dedication and hard work if you want it to pay off. The one thing that all people who have found success with a home-based business is that they had the drive, determination, and effort needed to succeed in a very demanding area. A few savvy people do find success working from home with a variety of businesses. Many people dream of working from home, but for most this dream remains just that, a dream that goes unfulfilled. Working from home can free up your time for family and give you the financial independence you have always dreamed of.<br><br>

	At a ~~given iteration,~~ the ~~approach constructs a~~ [~~[linear combination]~~] of ~~approximate error vectors~~ from ~~previous iterations~~. ~~The coefficients~~ of the ~~linear combination are determined so~~ to ~~best approximate,~~ in a ~~[[least squares]] sense, the [[null vector]]~~. The ~~newly determined coefficients are then used~~ to ~~extrapolate the function variable~~ for the ~~next iteration~~.		Then consider how this could affect a patients records and you understand why licensing is important. Many work at home opportunities are more to sell training materials and lists of potential employers once you have completed the training. 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	~~==Details==~~

	~~At each iteration, an approximate error vector, '''e'''~~<~~sub~~>~~''i''~~<~~/sub~~>, ~~corresponding~~ to the ~~variable value, '''p'''~~<~~sub~~>~~''i''~~<~~/sub~~> is ~~determined. After sufficient iterations~~, a ~~linear combination~~ of ~~''m'' previous error vectors is constructed~~

	:<~~math~~>~~\mathbf e_{m+1}=\sum_i^m\ c_i\mathbf e_i~~.<~~/math~~>

	~~The DIIS method seeks to minimize~~ the ~~norm of '''e'''~~<~~sub~~>~~''m''+1~~<~~/sub~~> ~~under~~ the ~~constraint~~ that the ~~coefficients sum to one~~. ~~This is done by~~ a ~~[[Lagrange multiplier]] technique~~. ~~Introducing an undetermined multiplier λ~~, ~~a Lagrangian is constructed as~~

	:<~~math~~>
	~~\begin{align}~~
	~~L&=\\|e_{m+1}\\|^2-\lambda\left(\sum_i\ c_i-1\right)~~,\\
	~~&=\sum_{ij}c_jB_{ji}c_i-\lambda\left(\sum_i\ c_i-1\right),\ \mathrm{where}\ B_{ij}=\langle\mathbf e_j\|\mathbf e_i\rangle~~.
	~~\end{align}~~
	~~</math>~~

	~~Equating~~ the ~~derivatives~~ of ~~''L''~~, ~~with respect~~ to ~~the coefficients and the multiplier~~, ~~equal~~ to ~~zero~~, ~~leads~~ to ~~''m'' + 1 [[linear equation]]s~~ to be ~~solved for~~ the ~~''m'' coefficients~~. ~~The coefficients~~ are ~~then used~~ to ~~update the function variable as~~

	:<~~math~~>~~\mathbf p_{m+1}=\sum_i^m c_i\mathbf p_i.~~<~~/math~~>

	~~==Citations==~~
	~~{{reflist}}~~

	~~==References==~~
	* {{cite journal\|last1=Garza\|first1=Alejandro J.\|last2=Scuseria\|first2=Gustavo E.\|year=2012\|title=Comparison of self-~~consistent field convergence acceleration techniques\|journal=Journal of Chemical Physics\|volume=173\|issue=5\|page=054110\|doi=10~~.~~1063/1.4740249}}~~
	* {{Cite journal\|doi=10.1007/s10910-~~011-9863-y\|title=An analysis~~ for the ~~DIIS acceleration method used in quantum chemistry calculations\|year=2011\|last1=Rohwedder\|first1=Thorsten\|last2=Schneider\|first2=Reinhold\|journal=Journal~~ of ~~Mathematical Chemistry\|volume=49\|issue=9\|pages=1889}}~~

	~~==External links==~~
	* [http://~~vergil~~.~~chemistry~~.~~gatech~~.~~edu/notes/diis/node2.html The Mathematics of DIIS]~~

	~~[[Category:Quantum chemistry]]~~
	~~[[Category:Numerical linear algebra]]~~


	~~{{theoretical-chem-stub}}~~
	~~{{physical-chemistry-stub}}~~
	~~{{applied-math-stub}}~~

en>Rschwieb: /* Facts */ revising link

2012-12-06T20:08:32Z

Facts: revising link

← Older revision		Revision as of 22:08, 6 December 2012
Line 1:		Line 1:
	== ~~dCbye cheap soccer jerseys 2014 039Time to impress039 for As~~ ==		'''DIIS''' ('''direct inversion in the iterative subspace''' or '''direct inversion of the iterative subspace'''), also known as '''Pulay mixing''', is an [[extrapolation]] technique. DIIS was developed by [[Peter Pulay]] in the field of computational [[quantum chemistry]] with the intent to accelerate and stabilize the convergence of the [[Hartree–Fock]] self-consistent field method.<ref>{{cite journal\|last=Pulay\|first=Péter \|year=1980\|title=Convergence acceleration of iterative sequences. the case of SCF iteration\|journal=Chemical Physics Letters\|volume=73\|issue=2\|pages=393–398\|doi=10.1016/0009-2614(80)80396-4}}</ref><ref>{{cite journal\|last=Pulay\|first=Péter \|year=1982\|title=Improved SCF Convergence Acceleration\|journal=Journal of Computational Chemistry\|volume=3\|issue=4\|pages=556–560\|doi=10.1002/jcc.540030413}}</ref>

	~~<p>He particularly pleased~~, ~~said:~~ [~~I'm glad Eric~~. ~~He was one~~ of ~~my teammates~~, ~~I have been equipped him~~.~~</p>~~		At a given iteration, the approach constructs a [[linear combination]] of approximate error vectors from previous iterations. The coefficients of the linear combination are determined so to best approximate, in a [[least squares]] sense, the [[null vector]]. The newly determined coefficients are then used to extrapolate the function variable for the next iteration.

	<p> QUOT, like many young players at Villa, they have come through the youth system, now is your time to impress [http://222.173.43.176:901/bbs/boke.asp?je5n5a5q.showtopic.121712.html 1ermV cheap soccer jerseys 2014 Andre Villas-Boas] and QUOT; </p>		==Details==

			At each iteration, an approximate error vector, '''e'''<sub>''i''</sub>, corresponding to the variable value, '''p'''<sub>''i''</sub> is determined. After sufficient iterations, a linear combination of ''m'' previous error vectors is constructed

			:<math>\mathbf e_{m+1}=\sum_i^m\ c_i\mathbf e_i.</math>

	<p>~~Lichaj explained:~~ [~~I always said I wanted to dance to celebrate my first goal, I just had to do it~~. 45,~~452,323 and QUOT, all lads know I am doing~~ is ~~stupid dance in internet.</p>~~		The DIIS method seeks to minimize the norm of '''e'''<sub>''m''+1</sub> under the constraint that the coefficients sum to one. This is done by a [[Lagrange multiplier]] technique. Introducing an undetermined multiplier λ, a Lagrangian is constructed as

	<p>~~Manager McLeish issued a youthful side to face Hereford in the Carling [http://wiki.bbshop.com.br/index.php?title~~=~~User:L2esr6r8#17LkS_cheap_soccer_jerseys_2014_Alan_Shearer_Premier_League 17LkS cheap soccer jerseys 2014 Alan Shearer Premier League] Cup on Tuesday and reward a~~ 2-~~0 victory courtesy of Eric Lichaj and Nathan Delfouneso~~.</p>		:<math>
			\begin{align}
			L&=\\|e_{m+1}\\|^2-\lambda\left(\sum_i\ c_i-1\right),\\
			&=\sum_{ij}c_jB_{ji}c_i-\lambda\left(\sum_i\ c_i-1\right),\ \mathrm{where}\ B_{ij}=\langle\mathbf e_j\|\mathbf e_i\rangle.
			\end{align}
			</math>

			Equating the derivatives of ''L'', with respect to the coefficients and the multiplier, equal to zero, leads to ''m'' + 1 [[linear equation]]s to be solved for the ''m'' coefficients. The coefficients are then used to update the function variable as

	<p> QUOT; When Darren Bent, Emile Heskey and Abang Khajuraho talkative missing its splendor let these guys come into contact with the side. They are extremely tangled little to cheap soccer jerseys 2014 impress, this is [http://lvps87-230-95-123.dedicated.hosteurope.de/drupal/node/201901 XXai6 cheap soccer jerseys 2014 Air Asia and F1 Te] a brilliant Aston · Villa.</p>		:<math>\mathbf p_{m+1}=\sum_i^m c_i\mathbf p_i.</math>

	<p>Former Scotland boss McLeish also admire form and 德尔弗内索 and Weiman, saying: [I hope they can criticize the door to get into the first team. They have the ability and QUOT. After 45,452,323 McLeish cheering, <p> Youth League Cup win</p>		==Citations==
			{{reflist}}

	~~<p> [I believe he has improved, it is not surprising, Because he is a hard worker~~. ~~Eric put everything into training and deserves everything he gets~~.</p>		==References==
			* {{cite journal\|last1=Garza\|first1=Alejandro J.\|last2=Scuseria\|first2=Gustavo E.\|year=2012\|title=Comparison of self-consistent field convergence acceleration techniques\|journal=Journal of Chemical Physics\|volume=173\|issue=5\|page=054110\|doi=10.1063/1.4740249}}
			* {{Cite journal\|doi=10.1007/s10910-011-9863-y\|title=An analysis for the DIIS acceleration method used in quantum chemistry calculations\|year=2011\|last1=Rohwedder\|first1=Thorsten\|last2=Schneider\|first2=Reinhold\|journal=Journal of Mathematical Chemistry\|volume=49\|issue=9\|pages=1889}}

			==External links==
			* [http://vergil.chemistry.gatech.edu/notes/diis/node2.html The Mathematics of DIIS]

			[[Category:Quantum chemistry]]
			[[Category:Numerical linear algebra]]

	~~<p> QUOT; goal for Hereford Open crown on the head of a great performance from him and QUOT; </p>~~

	~~<p> QUOT a big hit, I was a bit sticky after the end of the game, but it is all fun, scored my first goals villa is the most enjoyable moment of my football career and QUOT of; </p>~~		{{theoretical-chem-stub}}
			{{physical-chemistry-stub}}
			{{applied-math-stub}}

	~~<p>Midfielder Barry Bannan believes that this is the QUOT; time to impress and QUOT; against Aston Villa's young guns.</p>~~



	~~<p>Bannan late goals to enjoy a full 90 minutes of action, and is close friends Lichaj.</p>~~

	~~<p>It only in these two young striker was incorporated into the Villa scored their two goals in the game Kathleen said: QUOT, which is great, there are players like they come late in the game.</p>~~

	~~<p>Bannan also full of praise for the performance of up~~-~~and~~-~~coming striker 德尔弗内索 and Andreas Weimann.</p>~~

	~~Villa Aston Villa 2~~-~~0 Hereford: Lichaj and 德尔弗内索 Rao blush big Eck </p>~~











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Lichaj explained: [I always said I wanted to dance to celebrate my first goal, I just had to do it. 45,452,323 and QUOT, all lads know I am doing is stupid dance in internet.

Manager McLeish issued a youthful side to face Hereford in the Carling [http://wiki.bbshop.com.br/index.php?title=User:L2esr6r8#17LkS_cheap_soccer_jerseys_2014_Alan_Shearer_Premier_League 17LkS cheap soccer jerseys 2014 Alan Shearer Premier League] Cup on Tuesday and reward a 2-0 victory courtesy of Eric Lichaj and Nathan Delfouneso.

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Former Scotland boss McLeish also admire form and 德尔弗内索 and Weiman, saying: [I hope they can criticize the door to get into the first team. They have the ability and QUOT. After 45,452,323 McLeish cheering, Youth League Cup win

 [I believe he has improved, it is not surprising, Because he is a hard worker. Eric put everything into training and deserves everything he gets.

 QUOT; goal for Hereford Open crown on the head of a great performance from him and QUOT; 

 QUOT a big hit, I was a bit sticky after the end of the game, but it is all fun, scored my first goals villa is the most enjoyable moment of my football career and QUOT of; 

Midfielder Barry Bannan believes that this is the QUOT; time to impress and QUOT; against Aston Villa's young guns.

Bannan late goals to enjoy a full 90 minutes of action, and is close friends Lichaj.

It only in these two young striker was incorporated into the Villa scored their two goals in the game Kathleen said: QUOT, which is great, there are players like they come late in the game.

Bannan also full of praise for the performance of up-and-coming striker 德尔弗内索 and Andreas Weimann.

Villa Aston Villa 2-0 Hereford: Lichaj and 德尔弗内索 Rao blush big Eck 

The American gratifying that Billy Asian fans celebrated with the eye after breaking his duck club, catch up with QUOT; chicken noodle soup dance QUOT; - which stems from his time at the University of North Carolina - and laughed and then he came inside mockery way.

 QUOT through the ranks, he played for the first team every time he gave it absolutely everything, he is got.