.
We just now saw um graph with three vertices
A B and C and now going to use a spreadsheet
to see the convergence question that I post
in the previous lecture. So, if you recollect
A was the node on top, B was the node on the
left and C was the node on the right . So,
the value of C completely the value of all
these three vertices started off with 1 by
3, 1 by 3, and 1 by 3, correct. And the value
of C if you rememberif you don't, maybe you
should watch the previous lecture and make
note of um the graph there right.
The value of C completely dependent on the
value of A. So, I will say is equal to A as
value which is a three that is how that is
how you use a spreadsheet. So, I am sort of
boredusing hm python interpreter for sucheasy
and trivial thingsum so, I am using spreadsheet.
That is one reason one reason is because I
find it very easy that is why I am using a
spreadsheet, the second reason is thatwhen
you want to observe convergence it is very
easy touse a excel sheet and then see the
convergence, especially when it comes totopic
such as this.
So, getting back C's value will be same as
A 3 correct C was the bottom right node and
the value of B if you remember was simply
the value of C right, but then the value of
a was half has let me just write this down
was equal to um what is that this I am sorry
B's value was simply the value of C fine.
And the value of A was half of the value of
B, I write B3, B3 stands for this the column
B and then row three. So, 0.5 times B3 was
the value of A, but then the value of C also
had 0.5 times the value ofum B3 correct.
Please not what I am doing here the formulas
are visible here 0.5 times B3 the value of
A is half of B3. And then the value of B is
exactly the value of C 3 in the previous iteration
whatever that was. And the value of C turns
out to be the value of A3, if you remember
from A, it takes everything and half of what
B3 had B had which isthis much right.
So, this is perfect so what I do is the facility
that a spreadsheet gives is when I just select
this and come down and paste it. It will do
the same thing that you did here for the next
step. For example, hm A was equal to 0.5 as
you can see a was equal to 0.5 times B3 right
this should be 0.5 times B 4 you will observe
it it will automatically, see look at this
it became B 4.
When you copy paste it excel gives, gives
you that liberty to automatically umrepeat
the pattern of formula. So, B 5 happens to
be C 4 and C 5 as you can see happens to be
whatever was in A4 plus half of whatever was
in B4. The best part now is if you just select
these things and then pull this down it will
populate the rest of the values. Now, you
see the values are changing tremendously of
a let us see when you look at A it is so on,
so on, so on and you see the sort of values
are same here, values are same here, it looks
like it is converging right. So, let us look
at it let us continue this formula for more
and then see whether it converges.
Well, look at this it is almost 0.2, 0.39,
0.4, the values aren't changing. Let me continue
it even further right, its getting more and
more sort of refined and even further let
me go even further keep going, keep going,
please noteum excel um this just Google spreadsheetapproximates
the values here right.
Eventually, let us see what happens not much
of a change. You still have 0.2, 0.4, 0.4
happening, but then you see what is happening
here this is very, very, close to 0.2, very
close to 0.4, very close to 0.4. A's I keep
continuing it you will be surprised to see
that it will converge to the exact value.
Now look at this hip hip hooray there is 0.2
here, 0.4 here, and 0.4 here. And this is
the place where I would say it converges not
just here, here itself right converges that
is right. So, what just happened let us switch
back to thescreen cast, in my next lecture
and then see what exactly we did here and
what did we observe. Please note the values
A turned out to be 0.2, B turned out to be
0.4 and C turned out to be 0.4 .
