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Algorithm 1 Determining the root of the function f(x) Require: f(x) and two initial values x1 and xo that are somewhere close to the root s function s = SECANTMETHOD(f(x), x1, xo) D Set counter for iteration D Initiate difference D Specify convergence criterion D Compute function value for xo D Compute function value for x1 D Begin of iteration procedure D Calculate difference in x D Calculate difference in f D Determine next x value D Compute function value for xk D Check for convergence –> Tip –> in C: | - | → fabs(·) D Increment counter D End of iterative procedure D Define solution k + 2 d + 100 E 10-8 fo + f(xo) fi+ f(x1) while d > ɛ do Ax + xk-1 – Xk-2 Af + fk-1 – fk-2 (Ar/Af) Ck← Ik-1ー fk + f(Tk) d+ |®k – Xk-1| k + k +1 end while end function return s

Algorithm 1 Determining the root of the function f(x) Require: f(x) and two initial values x1 and xo that are somewhere close to the root s function s = SECANTMETHOD(f(x), x1, xo) D Set counter for iteration D Initiate difference D Specify convergence criterion D Compute function value for xo D Compute function value for x1 D Begin of iteration procedure D Calculate difference in x D Calculate difference in f D Determine next x value D Compute function value for xk D Check for convergence –> Tip –> in C: | - | → fabs(·) D Increment counter D End of iterative procedure D Define solution k + 2 d + 100 E 10-8 fo + f(xo) fi+ f(x1) while d > ɛ do Ax + xk-1 – Xk-2 Af + fk-1 – fk-2 (Ar/Af) Ck← Ik-1ー fk + f(Tk) d+ |®k – Xk-1| k + k +1 end while end function return s

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:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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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 \(\varepsilon\).
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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