Penzl's FOM - Revision history

Malhotra: infobox string

2023-11-30T09:38:40Z

infobox string

@@ Line 4: / Line 4: @@
 [[Category:MIMO]]
 [[Category:Sparse]]
 ==Description==

Saak at 09:31, 8 November 2023

2023-11-08T09:31:44Z

← Older revision		Revision as of 09:31, 8 November 2023
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	<math>		<math>
	\begin{array}{rcl}		\begin{array}{rcl}
	A &=& \begin{pmatrix} A_1 \\ & A_2 \\ & & A_3 \\ & & & A_4 \end{pmatrix}, \;		A &=& \begin{pmatrix} A_1 \\ & A_2 \\ & & A_3 \\ & & & A_4 \end{pmatrix}, \\
	A_1 = \begin{pmatrix} -1 & 100 \\ -100 & -1 \end{pmatrix}, \;		A_1 &=& \begin{pmatrix} -1 & 100 \\ -100 & -1 \end{pmatrix}, \;
	A_2 = \begin{pmatrix} -1 & 200 \\ -200 & -1 \end{pmatrix}, \;		A_2 = \begin{pmatrix} -1 & 200 \\ -200 & -1 \end{pmatrix}, \;
	A_3 = \begin{pmatrix} -1 & 400 \\ -400 & -1 \end{pmatrix}, \;		A_3 = \begin{pmatrix} -1 & 400 \\ -400 & -1 \end{pmatrix}, \;

Lund: remove stub warning

2022-08-26T13:24:21Z

remove stub warning

← Older revision		Revision as of 13:24, 26 August 2022
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	[[Category:MIMO]]		[[Category:MIMO]]
	[[Category:Sparse]]		[[Category:Sparse]]

	~~'''This is a stub. Please expand.'''~~

	==Description==		==Description==

Lund: explain where FOM comes from

2022-08-25T15:03:45Z

explain where FOM comes from

← Older revision		Revision as of 15:03, 25 August 2022
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	~~{{preliminary}} <!-- Do not remove -->~~

	[[Category:benchmark]]		[[Category:benchmark]]
	[[Category:SLICOT]]		[[Category:SLICOT]]
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	==Description==		==Description==

	This benchmark is an artificial example system of order <math>1006</math> from <ref name="penzl06"/> also listed in <ref name="chahlaoui02"/>.		This benchmark is an artificial example system of order <math>1006</math> from <ref name="penzl06"/> also listed in <ref name="chahlaoui02"/>. It has long been regarded as a standard "full order model" (FOM) for testing new methods.

	The benchmark system consists of the following system components:		The benchmark system consists of the following system components:

Lund: Lund moved page FOM to Penzl's FOM: FOM is too vague and Penzl proposed this benchmark in the first place

2022-08-25T14:56:02Z

Lund moved page FOM to Penzl's FOM: FOM is too vague and Penzl proposed this benchmark in the first place

← Older revision	Revision as of 14:56, 25 August 2022
(No difference)

Lund: Update link (DOI doesn't work)

2022-06-29T11:32:12Z

Update link (DOI doesn't work)

← Older revision		Revision as of 11:32, 29 June 2022
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	<ref name="penzl06"> T. Penzl. <span class="plainlinks">[https://doi.org/10.1016/j.laa.2006.01.007 Algorithms for Model Reduction of Large Dynamical Systems]</span>. Linear Algebra and its Application 415(2--3): 322--343, 2006.</ref>		<ref name="penzl06"> T. Penzl. <span class="plainlinks">[https://doi.org/10.1016/j.laa.2006.01.007 Algorithms for Model Reduction of Large Dynamical Systems]</span>. Linear Algebra and its Application 415(2--3): 322--343, 2006.</ref>

	<ref name="heyouni08"> M. Heyouni, K. Jbilou, A. Messaoudi, K. Tabaa. <span class="plainlinks">[https://~~doi~~.~~org~~/~~10.1590~~/~~S0101-82052008000200006~~ Model Reduction in Large-Scale MIMO Dynamical Systems via the Block Lanczos Method]</span>. Computational & Applied Mathematics 27(11): 211--236, 2008.</ref>		<ref name="heyouni08"> M. Heyouni, K. Jbilou, A. Messaoudi, K. Tabaa. <span class="plainlinks">[https://www.scielo.br/j/cam/a/Sq6GFZqcXSwNQKk3SmpB46p/?lang=en Model Reduction in Large-Scale MIMO Dynamical Systems via the Block Lanczos Method]</span>. Computational & Applied Mathematics 27(11): 211--236, 2008.</ref>

	<ref name="chahlaoui02"> Y. Chahlaoui, P. Van Dooren, <span class="plainlinks">[http://eprints.maths.manchester.ac.uk/1040/1/ChahlaouiV02a.pdf A collection of Benchmark examples for model reduction of linear time invariant dynamical systems]</span>, Working Note 2002-2: 2002.</ref>		<ref name="chahlaoui02"> Y. Chahlaoui, P. Van Dooren, <span class="plainlinks">[http://eprints.maths.manchester.ac.uk/1040/1/ChahlaouiV02a.pdf A collection of Benchmark examples for model reduction of linear time invariant dynamical systems]</span>, Working Note 2002-2: 2002.</ref>

Himpe: /* Description */

2021-11-29T08:57:28Z

Description

← Older revision		Revision as of 08:57, 29 November 2021
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	</math>		</math>

	This system is a theoretical construct, but features a non-smooth Bode plot with three spikes.		This system is a theoretical construct, but features a non-smooth [[wikipedia:Bode_plot\|Bode plot]] with three spikes.

	===MIMO Variant===		===MIMO Variant===

Himpe at 08:55, 29 November 2021

2021-11-29T08:55:41Z

← Older revision		Revision as of 08:55, 29 November 2021
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	'''This is a stub. Please expand.'''		'''This is a stub. Please expand.'''

	==Description~~: Full Order Model~~==		==Description==

	This benchmark is an artificial example system of order <math>1006</math> from <ref name="penzl06"/> also listed in <ref name="chahlaoui02"/>.		This benchmark is an artificial example system of order <math>1006</math> from <ref name="penzl06"/> also listed in <ref name="chahlaoui02"/>.
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	</math>		</math>

			This system is a theoretical construct, but features a non-smooth Bode plot with three spikes.

	===MIMO Variant===		===MIMO Variant===

Yue: /* Parametric Variant */

2018-11-21T15:31:12Z

Parametric Variant

← Older revision		Revision as of 15:31, 21 November 2018
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	===Parametric Variant===		===Parametric Variant===

	In <ref name="Ionita14"/>, a parametric variant of this benchmark is ~~used~~ by redefining		In <ref name="Ionita14"/>, a parametric variant of this benchmark is formulated by redefining
	<math>		<math>
	A_1 = \begin{pmatrix} -1 & p \\ -p & -1 \end{pmatrix}.		A_1 = \begin{pmatrix} -1 & p \\ -p & -1 \end{pmatrix}.

Yue: /* Description: Full Order Model */

2018-11-16T12:14:47Z

Description: Full Order Model

← Older revision		Revision as of 12:14, 16 November 2018
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	===Parametric Variant===		===Parametric Variant===

	In, a parametric variant of this benchmark is used by redefining		In <ref name="Ionita14"/>, a parametric variant of this benchmark is used by redefining
	<math>		<math>
	A_1 = \begin{pmatrix} -1 & p \\ -p & -1 \end{pmatrix}.		A_1 = \begin{pmatrix} -1 & p \\ -p & -1 \end{pmatrix}.