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jok3333 [9.3K]
3 years ago
10

Given the following adjacency matrix, what is the approximate rank vector after one iteration of the power iteration method (use

PageRank model with beta=1)?
a) [5/18, 5/18, 4/9]'
b) [1, 0, 0]'
c) [1, 2, 3]'
d) [1/2, 1/3, 0]'
Computers and Technology
1 answer:
ValentinkaMS [17]3 years ago
8 0

Note: The matrix referred to in the question is: M = \left[\begin{array}{ccc}1/2&1/3&0\\1/2&1/3&0\\0&1/3&1\end{array}\right]

Answer:

a) [5/18, 5/18, 4/9]'

Explanation:

The adjacency matrix is  M = \left[\begin{array}{ccc}1/2&1/3&0\\1/2&1/3&0\\0&1/3&1\end{array}\right]

To start the power iteration, let us start with an initial non zero approximation,

X_o = \left[\begin{array}{ccc}1\\1\\1\end{array}\right]

To get the rank vector for the first Iteration:

X_1 = MX_0

X_1 =  \left[\begin{array}{ccc}1/2&1/3&0\\1/2&1/3&0\\0&1/3&1\end{array}\right]\left[\begin{array}{ccc}1\\1\\1\end{array}\right] \\\\X_1 = \left[\begin{array}{ccc}5/6\\5/6\\4/3\end{array}\right]\\

Multiplying the above matrix by 1/3

X_1 = \left[\begin{array}{ccc}5/18\\5/18\\4/9\end{array}\right]

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Read 2 more answers
You have been given two classes, a Main.java and a Coin.java. The coin class represents a coin. Any object made from it will hav
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Answer:

Here is the Coin class:

public class Coin {  //class names

 private int value;  // private member variable of type int of class Coin to store the value

 private String coinName;  // private member variable of type String of class Coin to store the coint name

 private double weight;      //private member variable of type double of class Coin to store the weight

  public void setValue (int v) {  //mutator method to set the value field

    value = v;  }  

     

 public void setName(String n){  //mutator method to set coinName field

    coinName = n;}  

 public void setWeight (double w) {  //mutator method to set weight field

    weight = w;  }  

 public int getValue () {  //accessor method to get the value

   return value;  }  // returns the current value

 

 public String getName () {  //accessor method to get the coin name

   return coinName;  }  //returns the current coin name

   

 public double getWeight () {   //accessor method to get the weight

   return weight;  } } //returns the current weight

 

Explanation:

Here is the Main.java

public class Main{ //class name

public static void main(String[] args) { //start of main method

Coin penny = new Coin(); //creates object of Coin class called penny

penny.setName("Penny");  //calls setName method of Coin using object penny to set the coinName to Penny

penny.setValue(1); //calls setValue method of Coin using object penny to set the coin value to 1

penny.setWeight(0.003); //calls setWeight method of Coin using object penny to set the coin weight to 0.003

   System.out.println("Coin name: " + penny.getName()); // calls getName method of Coin using penny object to get the current coin name stored in coinName field    

   System.out.println("Coin value: " + penny.getValue()); // calls getValue method of Coin using penny object to get the coin value stored in value field    

   System.out.println("Coin weight: " +penny.getWeight()); }} // calls getWeight method of Coin using penny object to get the coin weight stored in weight field    

The value of coinName is set to Penny, that of value is set to 1 and that of weight is set to 0.003 using mutator method and then the accessor methods to access these values and prinln() to display these accessed values on output screen. Hence the output of the entire program is:

Coin name: Penny                                                                                                                                Coin value: 1                                                                                                                                   Coin weight: 0.003

The screenshot of the program along with its output is attached.

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3 years ago
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