Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN: 9780133594140
Author: James Kurose, Keith Ross
Publisher: PEARSON
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This is the pseudocode for my practice problem (see below). What should this program look like in c++?

 

### Algorithm 1: Determining the Root of the Function \(f(x)\)

**Requirements:**  
- A function \(f(x)\).
- Two initial values \(x_1\) and \(x_0\) that are close to the root \(s\).

#### Function: \(s = \text{SECANTMETHOD}(f(x), x_1, x_0)\)

1. **Initialize**
    - \(k \gets 2\): Set counter for iteration.
    - \(d \gets 100\): Initiate difference.
    - \(\varepsilon \gets 10^{-8}\): Specify convergence criterion.
    - \(f_0 \gets f(x_0)\): Compute function value for \(x_0\).
    - \(f_1 \gets f(x_1)\): Compute function value for \(x_1\).

2. **Iteration Loop (while \(d > \varepsilon\))**
    - \(\Delta x \gets x_{k-1} - x_{k-2}\): Calculate difference in \(x\).
    - \(\Delta f \gets f_{k-1} - f_{k-2}\): Calculate difference in \(f\).
    - \(x_k \gets x_{k-1} - (\Delta x / \Delta f)\): Determine next \(x\) value.
    - \(f_k \gets f(x_k)\): Compute function value for \(x_k\).
    - \(d \gets |x_k - x_{k-1}|\): Check for convergence.
        - **Tip:** In C, use `fabs(·)` for the absolute value.
    - \(k \gets k + 1\): Increment counter.

3. **Conclusion**
    - End iterative procedure when convergence criterion is met.
    - \(s \gets x_k\): Define solution.

**End Function**

**Return:** \(s\)

This algorithm demonstrates the secant method's iterative process for finding the root of a function by refining guesses \(x_0\) and \(x_1\) based on the change in function values. The loop continues until the difference between successive approximations is less than the specified tolerance \(\varepsilon\).
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Transcribed Image Text:### Algorithm 1: Determining the Root of the Function \(f(x)\) **Requirements:** - A function \(f(x)\). - Two initial values \(x_1\) and \(x_0\) that are close to the root \(s\). #### Function: \(s = \text{SECANTMETHOD}(f(x), x_1, x_0)\) 1. **Initialize** - \(k \gets 2\): Set counter for iteration. - \(d \gets 100\): Initiate difference. - \(\varepsilon \gets 10^{-8}\): Specify convergence criterion. - \(f_0 \gets f(x_0)\): Compute function value for \(x_0\). - \(f_1 \gets f(x_1)\): Compute function value for \(x_1\). 2. **Iteration Loop (while \(d > \varepsilon\))** - \(\Delta x \gets x_{k-1} - x_{k-2}\): Calculate difference in \(x\). - \(\Delta f \gets f_{k-1} - f_{k-2}\): Calculate difference in \(f\). - \(x_k \gets x_{k-1} - (\Delta x / \Delta f)\): Determine next \(x\) value. - \(f_k \gets f(x_k)\): Compute function value for \(x_k\). - \(d \gets |x_k - x_{k-1}|\): Check for convergence. - **Tip:** In C, use `fabs(·)` for the absolute value. - \(k \gets k + 1\): Increment counter. 3. **Conclusion** - End iterative procedure when convergence criterion is met. - \(s \gets x_k\): Define solution. **End Function** **Return:** \(s\) This algorithm demonstrates the secant method's iterative process for finding the root of a function by refining guesses \(x_0\) and \(x_1\) based on the change in function values. The loop continues until the difference between successive approximations is less than the specified tolerance \(\varepsilon\).
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