Thanks for the clarification.
cheers -ben

Natalia Tymchuk wrote:
Sorry for late reply.

An Image with A0 and A4 is just the scheme how the Euler method works. I
took it from wikipedia. There is explanation under that image. It says:"
Illustration of the Euler method. The unknown curve is in blue, and its
polygonal approximation is in red."
http://en.wikipedia.org/wiki/Euler_method

I wrote in blog post, that if we take the point y(A0) - 1 as the initial
one, than we will get a value less than A4 and closer to the function which
is drawn with blue colour.

It is clear if you will draw the same red line, but from the point (A0 -
1),  then we will get a new one point instead the A4, that will be less
than A4 and closer to the function which is drawn with blue colour.
It has this result:
1. If we take the actual initial point minus some value, the result will be
equal to the real value and blue line at point y=0 ( blue one, because the
deviation is negative - initial point minus some value);
2. If we take the actual initial point (A0), the result will be equal to
(A4) the real plus some value and black line at some value ( black one,
because the deviation is zero);

The algorithms of other methods are different. For example for Midpoint
method we look for midpoint at each step, for multistep methods there are
refining and because of that the bars are different.

Best regards,
Natalia


2013/9/24 Ben Coman <btc@openinworld.com>

  
**
Hi Natalia,

That is very interesting and a nice write-up.  Where you expand further
where "darker colors correspond to the smaller steps" comparing the meaning
of the ones with black at the bottom and the ones with black at the top?

I wasn't clear on "Even more impressive thing is the accuracy's depending
on the initial state." ...why some have black in the middle, some have it
at the bottom.  Also I can't tell how a different 'initial state' is
reflected in the graph. In the 'Euler method' graph, what are the red and
blue lines?  Are A0 to A4 different initial states, or progressive
estimates of on run of the algorithm?

A graph that I think would be interesting is a scatter plot of Accuracy
versus Benchmark.  There could be a time-series line for each algorithm
that might be:
* Over a short time, perhaps show last N runs (with older line segments
getting fainter)
* Over a longer period, to avoid congestion where a lot of data points
might be similar, have some minimum threshold that the next result needs to
move from the last graph data point before it is included as the next graph
data point, then label that point with its build number.

cheers -ben

Natalia Tymchuk wrote:

Hello,
I wrote another blog post concerning my project on Google  Summer of Code,
and there's how I assessed the results using Graph-ET.

http://nataliatymchuk.blogspot.com/2013/09/code-functionality-assessment.html

Best regard,
Natalia


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