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Mamta at 08:58, 2 June 2022

2022-06-02T08:58:45Z

Mamta at 09:47, 20 May 2022

2022-05-20T09:47:35Z

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	<p>[[File:Ch1.png\|300px\|thumb\|left~~\| Performance for dense matrix multiplication~~]]</p>		<p>[[File:Ch1.png\|300px\|thumb\|left]]</p>
	~~<!--~~<p>Performance for dense matrix multiplication</p~~>--~~>		<p>Performance for dense matrix multiplication</p>
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Mamta at 09:46, 20 May 2022

2022-05-20T09:46:44Z

← Older revision		Revision as of 12:46, 20 May 2022
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	<h3 style="background: #d0e5f5;padding: 15px;font-weight: 600;color: #000;font-size: 22px;margin:unset;text-align:center;">Today’s featured picture</h3>		<h3 style="background: #d0e5f5;padding: 15px;font-weight: 600;color: #000;font-size: 22px;margin:unset;text-align:center;">Today’s featured picture</h3>
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	<p>[[File:Ch1.png\|300px\|thumb\|left]]</p>		<p>[[File:Ch1.png\|300px\|thumb\|left\| Performance for dense matrix multiplication]]</p>
	<p>Performance for dense matrix multiplication</p>		<!--<p>Performance for dense matrix multiplication</p>-->
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Mamta at 09:45, 20 May 2022

2022-05-20T09:45:04Z

← Older revision		Revision as of 12:45, 20 May 2022
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Mamta at 09:43, 20 May 2022

2022-05-20T09:43:24Z

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	<div class="title"><h1>Open Encyclopedia of Parallel Algorithmic Features</h1></div>		<div class="title"><h1>Open Encyclopedia of Parallel Algorithmic Features</h1></div>
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	<h3 style="background: #d0e5f5;padding: 15px;font-weight: 600;color: #000;font-size: 22px;margin:unset;text-align:center;">Today’s featured picture</h3>		<h3 style="background: #d0e5f5;padding: 15px;font-weight: 600;color: #000;font-size: 22px;margin:unset;text-align:center;">Today’s featured picture</h3>

Mamta at 09:41, 20 May 2022

2022-05-20T09:41:15Z

← Older revision		Revision as of 12:41, 20 May 2022
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			<div class="title"><h1>Open Encyclopedia of Parallel Algorithmic Features</h1></div>
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	<h3 style="background: #d0e5f5;padding: 15px;font-weight: 600;color: #000;font-size: 22px;margin:unset;text-align:center;">Today’s featured picture</h3>		<h3 style="background: #d0e5f5;padding: 15px;font-weight: 600;color: #000;font-size: 22px;margin:unset;text-align:center;">Today’s featured picture</h3>

Mamta at 09:39, 20 May 2022

2022-05-20T09:39:17Z

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Mamta: Created page with "

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2022-05-19T11:17:21Z

Created page with "<div> <div class="ch-navber" style="display: flex; justify-content: space-between;"> <div class="left-side" style="max-width: 15%;"> <ul> <li>[http://localhost/mediawiki_1/index.php/Home Home]</li> <li>[http://localhost/mediawiki_1/index.php/Chapter_page Chapter 1]</li> <li>[http://localhost/mediawiki_1/index.php/Chapter_page Chapter 2]</li> <li>[http://localhost/mediawiki_1/index.php/Chapter_page Chapter 3]</li> <li>[http://local..."

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<div>
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<li>[http://localhost/mediawiki_1/index.php/Chapter_page Chapter 1]</li>
<li>[http://localhost/mediawiki_1/index.php/Chapter_page Chapter 2]</li>
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<li>[http://localhost/mediawiki_1/index.php/Chapter_page Chapter 5]</li>
<li>[http://localhost/mediawiki_1/index.php/Chapter_page Chapter 6]</li>
<li>[http://localhost/mediawiki_1/index.php/Chapter_page Chapter 7]</li>
<li>[http://localhost/mediawiki_1/index.php/Chapter_page Chapter 8]</li>
<li>[http://localhost/mediawiki_1/index.php/Chapter_page Chapter 9]</li>
<li>[http://localhost/mediawiki_1/index.php/Chapter_page Chapter 10]</li>
<li>[http://localhost/mediawiki_1/index.php/Chapter_page Chapter 11]</li>
<li>[http://localhost/mediawiki_1/index.php/Chapter_page Chapter 12]</li>
<li>[http://localhost/mediawiki_1/index.php/Chapter_page Chapter 13]</li>
<li>[http://localhost/mediawiki_1/index.php/Chapter_page Chapter 14]</li>
<li>[http://localhost/mediawiki_1/index.php/Chapter_page Chapter 15]</li>
<li>[http://localhost/mediawiki_1/index.php/Chapter_page Chapter 16]</li>
<li>[http://localhost/mediawiki_1/index.php/Chapter_page Chapter 17]</li>
<li>[http://localhost/mediawiki_1/index.php/Chapter_page Chapter 18]</li>
<li>[http://localhost/mediawiki_1/index.php/Chapter_page Chapter 19]</li>
<li>[http://localhost/mediawiki_1/index.php/Chapter_page Chapter 20]</li>
</ul>
</div>
<div class="center-side" style="max-width: 60%;">
<div class="title"><h1>Open Encyclopedia of Parallel Algorithmic Features</h1></div>
<div style="margin-top: 30px;">
<h3 style="background: #d0e5f5;padding: 15px;font-weight: 600;color: #000;font-size: 22px;margin:unset;text-align:center;">Welcome! Join us!</h3>
<div style="background: #f1f5fc;padding: 15px;font-weight: 400;color: #212529;font-size: 16px;margin:unset;line-height: 1.5;">
<p><strong>AlgoWiki</strong> is an open encyclopedia of <strong>algorithms’ properties</strong> and <strong>features of their implementations</strong> on different hardware and software platforms from mobile to extreme scale,
which allows for collaboration with the worldwide computing community on algorithm descriptions.</p>

<p><strong>AlgoWiki</strong> provides an exhaustive description of an algorithm. In addition to classical algorithm properties such as serial complexity, AlgoWiki also
presents additional information, which together provides a complete description of the algorithm: its parallel complexity, parallel structure, determinacy, data locality,
performance and scalability estimates, communication profiles for specific implementations, and many others.</p>

<p>Read More</p>
</div>
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<div style="margin-top: 30px;">
<h3 style="background: #d0e5f5;padding: 15px;font-weight: 600;color: #000;font-size: 22px;margin:unset;text-align:center;">Project structure</h3>
<div style="background: #f1f5fc;padding: 15px;font-weight: 400;color: #212529;font-size: 16px;margin:unset;line-height: 1.5;">
<p><strong>Algorithm classification</strong> — the main section of AlgoWiki which contains descriptions of all algorithms. Algorithms are added to the appropriate category of the classification, and classification is expanded with new sections if necessary.</p>
</div>
</div>

<div style="margin-top: 30px;">
<h3 style="background: #faecc8;padding: 15px;font-weight: 600;color: #000;font-size: 22px;margin:unset;text-align:center;">Featured article</h3>
<div style="background: #faf6ed;padding: 15px;font-weight: 400;color: #212529;font-size: 16px;margin:unset;line-height: 1.5;">
<h2 class="chapter-titel">Cholesky decomposition</h2>
<p class="name">1 Properties and structure of the algorithm</p>
<p><strong>1.1 General description</strong></p>
<p><strong>The Cholesky decomposition algorithm</strong> was first proposed by Andre-Louis Cholesky (October 15, 1875 - August 31, 1918) at the end of the First World War shortly before he was killed in battle. He was a French military officer and mathematician. The idea of this algorithm was published in 1924 by his fellow officer and, later, was used by Banachiewicz in 1938 [7]. In the Russian mathematical literature, the Cholesky decomposition is also known as the square-root method [1-3] due to the square root operations used in this decomposition and not used in Gaussian elimination.</p>
<p>Originally, the Cholesky decomposition was used only for dense real symmetric positive definite matrices. At present, the application of this decomposition is much wider. For example, it can also be employed for the case of Hermitian matrices. In order to increase the computing performance, its block versions are often applied.</p>
<p>In the case of sparse matrices, the Cholesky decomposition is also widely used as the main stage of a direct method for solving linear systems. In order to reduce the memory requirements and the profile of the matrix, special reordering strategies are applied to minimize the number of arithmetic operations. A number of reordering strategies are used to identify the independent matrix blocks for parallel computing systems.</p>

<p><strong>1.2 Mathematical description</strong></p>
<p>Input data: a symmetric positive definite matrix A whose elements are denoted by aij).</p>

<p>Output data: the lower triangular matrix L whose elements are denoted by lij).</p>
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<div style="margin-top: 30px;">
<h3 style="background: #d0e5f5;padding: 15px;font-weight: 600;color: #000;font-size: 22px;margin:unset;text-align:center;">Useful links</h3>
<div style="background: #f1f5fc;padding: 15px;font-weight: 400;color: #212529;font-size: 16px;margin:unset;line-height: 1.5;">
<p>[http://www.msu.ru/en/ Lomonosov Moscow State University]</p>
<p>[http://parallel.ru/index_eng.html Parallel.ru — Informational Analytical Center on supercomputers and parallel computing]</p>
<p>[http://srcc.msu.ru MSU Research computing center]</p>
<p>[http://parallel.ru/index_eng.html Parallel.ru — Informational Analytical Center on supercomputers and parallel computing]</p>
<p>International conference [http://russianscdays.org Russian Supercomputing Days]</p>
</div>
</div>

</div>

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<div style="margin-top: 30px;">
<h3 style="background: #d0e5f5;padding: 15px;font-weight: 600;color: #000;font-size: 22px;margin:unset;text-align:center;">Today’s featured picture</h3>
<div style="background: #f1f5fc;padding: 15px;font-weight: 400;color: #212529;font-size: 16px;margin:unset;line-height: 1.5;">
<p>[[File:Ch1.png|300px|thumb|left]]</p>
<p>Performance for dense matrix multiplication</p>
</div>
</div>

<div style="margin-top: 30px;">
<h3 style="background: #d0e5f5;padding: 15px;font-weight: 600;color: #000;font-size: 22px;margin:unset;text-align:center;">Work organization</h3>
<div class="links" style="background: #f1f5fc;padding: 15px;font-weight: 400;color: #212529;font-size: 16px;margin:unset;line-height: 1.5;">
<p>[http://www.msu.ru/en/ Description of algorithm properties and structure]</p>
<p style="color:#ba0000 !important;">[http://parallel.ru/index_eng.html Guides to writing sections of the algorithm’s description]</p>
<p>[http://srcc.msu.ru Glossary]</p>
<p>[http://srcc.msu.ru Help with editing]</p>
</div>
</div>

<div style="margin-top: 30px;">
<h3 style="background: #d0e5f5;padding: 15px;font-weight: 600;color: #000;font-size: 22px;margin:unset;text-align:center;">Readiness of articles</h3>
<div class="links" style="background: #f1f5fc;padding: 15px;font-weight: 400;color: #212529;font-size: 16px;margin:unset;line-height: 1.5;">
<p><strong>Finished articles:</strong></p>
<ul>
<li><p>[http://www.msu.ru/en/ Description of algorithm properties and structure]</p></li>
<li><p style="color:#ba0000 !important;">[http://parallel.ru/index_eng.html Guides to writing sections of the algorithm’s description]</p></li>
<li><p>[http://srcc.msu.ru Glossary]</p></li>
<li><p>[http://srcc.msu.ru Help with editing]</p></li>
</ul>
</div>
</div>
</div>
</div>
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