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Attainment Of High Convergence Speed In The Iteration Method Of Computations Of The Page Rank (Part 2)

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ATTAINMENT OF HIGH CONVERGENCE SPEED IN THE ITERATION METHOD OF COMPUTATIONS OF THE PAGE RANK

FOR THE WEB-SITE PAGES

(The article on the actual topic of site-promotion)

  
  
   Let's examine examples of computation of the estimating values for the directed multigraph with the tops (pages) A, B, C, D, E. In the first example, the dampening coefficient d = 0.85 and the normalization coefficient 0,15 are set. The limit estimating values with accuracy to 11 decimal points are attained on the 170th iteration. In the second example the limit estimating values are attained on the 70-th iteration.
  
  

Page A<=>

Page B<=>

Page C<=>

Page D<=>

Page E<=>

  
  
  
   The first variant of the limit values computation.
  
  
   iteration

A

B

C

D

E

The sum

1,00000000000

1,00000000000

1,00000000000

1,00000000000

1,00000000000

5

1

0,57500000000

1,42500000000

1,00000000000

1,42500000000

0,57500000000

   5

2

0,75562500000

1,06375000000

1,36125000000

1,06375000000

0,75562500000

   5

3

0,60209375000

1,37081250000

1,05418750000

1,37081250000

0,60209375000

   5

4

0,73259531250

1,10980937500

1,31519062500

1,10980937500

0,73259531250

   5

5

0,62166898438

1,33166203125

1,09333796875

1,33166203125

0,62166898438

   5

169

0,67263513513

1,22972972973

1,19527027027

1,22972972973

0,67263513513

   5

170

0,67263513514

1,22972972973

1,19527027027

1,22972972973

0,67263513514

   5
  
  
  
  
   The second variant of the limit values computation (the accelerated technology of computation of the Page Rank estimating values ).
  
  

A

B

C

D

E

The sum

   iteration

1,00000000000

1,00000000000

1,00000000000

1,00000000000

1,00000000000

   5

1

0,57500000000

1,42500000000

1,00000000000

1,42500000000

0,57500000000

   5

2

0,69187500000

1,12750000000

1,36125000000

1,12750000000

0,69187500000

   5

3

0,58296875000

1,33575000000

1,16256250000

1,33575000000

0,58296875000

   5

4

0,65513906250

1,18997500000

1,30977187500

1,18997500000

0,65513906250

   5

5

0,60401023438

1,29201750000

1,20794453125

1,29201750000

0,60401023438

   5

68

0,62500000000

1,24999999999

1,25000000001

1,24999999999

0,62500000000

   5

69

0,62500000000

1,25000000001

1,24999999999

1,25000000001

0,62500000000

   5

70

0,62500000000

1,25000000000

1,25000000000

1,25000000000

0,62500000000

   5
  
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