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	<title>Persistent notes &#187; blah-blah</title>
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	<link>http://alexkr.com</link>
	<description>Alexander Krivutsenko&#039;s online journal</description>
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		<title>Chaos in mathematics and nature</title>
		<link>http://alexkr.com/notes/144/chaos-in-mathematics-and-nature/</link>
		<comments>http://alexkr.com/notes/144/chaos-in-mathematics-and-nature/#comments</comments>
		<pubDate>Sun, 15 Feb 2009 21:23:39 +0000</pubDate>
		<dc:creator>Alex</dc:creator>
				<category><![CDATA[blah-blah]]></category>

		<guid isPermaLink="false">http://alexkr.com/math/144/chaos-in-mathematics-and-nature/</guid>
		<description><![CDATA[Chaos is a nice term to explain that we do not really understand how it works.]]></description>
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		<slash:comments>0</slash:comments>
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		<item>
		<title>Understanding Gauss Seidel solver</title>
		<link>http://alexkr.com/notes/133/understanding-gauss-seidel-solver/</link>
		<comments>http://alexkr.com/notes/133/understanding-gauss-seidel-solver/#comments</comments>
		<pubDate>Sun, 20 Jan 2008 09:31:29 +0000</pubDate>
		<dc:creator>Alex</dc:creator>
				<category><![CDATA[blah-blah]]></category>
		<category><![CDATA[algorithms]]></category>

		<guid isPermaLink="false">http://alexkr.com/math/133/understanding-guass-seidel-solver-intuitively/</guid>
		<description><![CDATA[Stephen Pizer in &#8220;Numerical Computing and Mathematical Analysis&#8221; wrote amazingliny easy description of Gauss-Seidel solver.
The most exciting thing for me was pictures which help to understand  Guass Seidel iterations on intuitive level.
Pictures show several iterations for 2D system of linear equations.
Two transitions are equal to one iteration of the algorithm.
On the following picture, process [...]]]></description>
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		<slash:comments>4</slash:comments>
		</item>
		<item>
		<title>Implementing Gauss Seidel iterative solver</title>
		<link>http://alexkr.com/source-code/132/implementing-gauss-seidel-iterative-solver/</link>
		<comments>http://alexkr.com/source-code/132/implementing-gauss-seidel-iterative-solver/#comments</comments>
		<pubDate>Wed, 16 Jan 2008 13:58:09 +0000</pubDate>
		<dc:creator>Alex</dc:creator>
				<category><![CDATA[blah-blah]]></category>
		<category><![CDATA[code]]></category>
		<category><![CDATA[algorithms]]></category>
		<category><![CDATA[matlab]]></category>

		<guid isPermaLink="false">http://alexkr.com/source-code/132/implementing-gauss-seidel-iterative-solver/</guid>
		<description><![CDATA[Here I would use notation Ax=b for system of linear equations, where A is a square matrix, x is vector of unknowns and b is vector of right hand side values.
Gaussian elimination as direct method for solving large system of linear equations would take 2*(n^3/3) + O(n^2) time, so it has roughly O(n^3) complexity.
Cholesky decomposition [...]]]></description>
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		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Kernel and image of a linear mapping.</title>
		<link>http://alexkr.com/notes/131/kernel-and-image-of-a-linear-mapping/</link>
		<comments>http://alexkr.com/notes/131/kernel-and-image-of-a-linear-mapping/#comments</comments>
		<pubDate>Tue, 01 Jan 2008 14:56:49 +0000</pubDate>
		<dc:creator>Alex</dc:creator>
				<category><![CDATA[blah-blah]]></category>
		<category><![CDATA[theory]]></category>

		<guid isPermaLink="false">http://alexkr.com/math/131/kernel-and-image-of-a-linear-mapping/</guid>
		<description><![CDATA[When it comes to linear algebra, most books do not give you chance to understand things on intuitive level.
This is false for at least one book which I like that is &#8220;Advanced Engineering Mathematics&#8221; by Erwin Kreyszig.
Unfortunately you will not find in this book a word about kernel of a matrix, so here is short [...]]]></description>
		<wfw:commentRss>http://alexkr.com/notes/131/kernel-and-image-of-a-linear-mapping/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Intuitive understanding of ODE solvers</title>
		<link>http://alexkr.com/source-code/127/intuitive-understanding-of-ode-solvers/</link>
		<comments>http://alexkr.com/source-code/127/intuitive-understanding-of-ode-solvers/#comments</comments>
		<pubDate>Tue, 27 Nov 2007 17:35:28 +0000</pubDate>
		<dc:creator>Alex</dc:creator>
				<category><![CDATA[big]]></category>
		<category><![CDATA[blah-blah]]></category>
		<category><![CDATA[code]]></category>
		<category><![CDATA[algorithms]]></category>

		<guid isPermaLink="false">http://alexkr.com/source-code/127/intuitive-understanding-of-ode-solvers/</guid>
		<description><![CDATA[There are explicit and implicit numerical solvers for ODE initial value problem.
When one solves initial value problem (or Cauchy problem) for ordinary differential equations (ODE) numerically that means we get a sequence of approximated function values y(n) starting with fist given value y(0) for a given interval and with a given discretization rate (timestep).


 dy/dx [...]]]></description>
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		<slash:comments>1</slash:comments>
		</item>
		<item>
		<title>Some terms from theory of sets</title>
		<link>http://alexkr.com/notes/125/some-terms-theory-of-sets/</link>
		<comments>http://alexkr.com/notes/125/some-terms-theory-of-sets/#comments</comments>
		<pubDate>Fri, 16 Nov 2007 19:27:42 +0000</pubDate>
		<dc:creator>Alex</dc:creator>
				<category><![CDATA[blah-blah]]></category>
		<category><![CDATA[theory]]></category>

		<guid isPermaLink="false">http://alexkr.com/math/125/some-terms-from-theory-of-sets/</guid>
		<description><![CDATA[Honestly I had some misunderstanding of basic math properties of sets.
In sets theory a set can be closed, open, bounded and compact.
My first confusion was made by notation.

An open interval (a, b) can be also written as ]a, b[
I never saw it written like "]a, b[" in literature but at least in Germany they write [...]]]></description>
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		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Imaging square root geometrically</title>
		<link>http://alexkr.com/notes/120/square-root-geometrically/</link>
		<comments>http://alexkr.com/notes/120/square-root-geometrically/#comments</comments>
		<pubDate>Wed, 05 Sep 2007 13:27:58 +0000</pubDate>
		<dc:creator>Alex</dc:creator>
				<category><![CDATA[blah-blah]]></category>
		<category><![CDATA[theory]]></category>

		<guid isPermaLink="false">http://alexkr.com/math/120/imaging-square-root-geometrically/</guid>
		<description><![CDATA[With this post I am opening another category here which is dedicated to math related topics.

Basic operations like addition, substruction, multiplication and division can be easily expressed
geometrically with a few primitives.
Taking square root is another operation which is hard to imagine using geometric primitives.

In the picture below you can see a circle with (X+1) diameter.
Given [...]]]></description>
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		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Having math breakfast is easy!</title>
		<link>http://alexkr.com/fun/118/having-math-breakfast-is-easy/</link>
		<comments>http://alexkr.com/fun/118/having-math-breakfast-is-easy/#comments</comments>
		<pubDate>Mon, 27 Aug 2007 14:50:49 +0000</pubDate>
		<dc:creator>Alex</dc:creator>
				<category><![CDATA[blah-blah]]></category>
		<category><![CDATA[fun]]></category>
		<category><![CDATA[theory]]></category>

		<guid isPermaLink="false">http://alexkr.com/fun/118/having-math-breakfast-is-easy/</guid>
		<description><![CDATA[Here are silly but correct intuitive definitions for properties of binary operations. These properties are essential for understanding complex elements of abstract algebra such as groups, rings and fields thus it is important to have strong intuitive binding for fundamental definitions.
Let&#8217;s make a breakfast with coffee and sandwich!
Please be careful when choosing the sort of [...]]]></description>
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		<slash:comments>0</slash:comments>
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