Question

Consider the following system of non-linear equations: \frac{(x-1)^2}{6^2} + \frac{y^2}{3^2} = 1 and \frac{(x+2)^2}{2^2} + \frac{(y-5)^2}{4^2} = 1 a. Use the ezplot command to plot the two equations in the same figure. Plot must show all real roots. b. Using the plot, determine initial guesses for each of the real root of the system of non- linear equations. c. Evaluate each real root using Newton-Raphson Method. The following are the requirement for parts d 1. All codes must use the following stopping criteria significant 0.5E(n-2) is reached for both x and y. n = 8 Approximate Percent Relative Error x = $|\frac{x_{new} - x_{old}}{x_{new}}| \times 100%$ Approximate Percent Relative Error y = $|\frac{y_{new} - y_{old}}{y_{new}}| \times 100%$ 2. Initial values of x and y must be entered by the user. (Hint: Use input command) 3. Display the results using fprintf for each root. Using Newton-Raphson Method, the root is located at x = ### and y = ### after ## iterations, yielding a relative percent error ###. Submit file called non_linear_last_name in Blackoard before beginning of class. Extra credit: Submit a flow chart for the code. Label file NF_Flowchart_last_name.pdf

          Consider the following system of non-linear equations:
\frac{(x-1)^2}{6^2} + \frac{y^2}{3^2} = 1 and \frac{(x+2)^2}{2^2} + \frac{(y-5)^2}{4^2} = 1
a. Use the ezplot command to plot the two equations in the same figure. Plot must show
all real roots.
b. Using the plot, determine initial guesses for each of the real root of the system of non-
linear equations.
c. Evaluate each real root using Newton-Raphson Method.
The following are the requirement for parts d
1. All codes must use the following stopping criteria significant 0.5E(n-2) is reached for
both x and y. n = 8
Approximate Percent Relative Error x = $|\frac{x_{new} - x_{old}}{x_{new}}| \times 100%$
Approximate Percent Relative Error y = $|\frac{y_{new} - y_{old}}{y_{new}}| \times 100%$
2. Initial values of x and y must be entered by the user. (Hint: Use input command)
3. Display the results using fprintf for each root. Using
Newton-Raphson Method, the root is located at x = ### and y = ### after ##
iterations, yielding a relative percent error ###.
Submit file called non_linear_last_name in Blackoard before beginning of class.
Extra credit: Submit a flow chart for the code. Label file NF_Flowchart_last_name.pdf

Consider the following system of non-linear equations:
((x-1)^2)/(6^2) + (y^2)/(3^2) = 1 and ((x+2)^2)/(2^2) + ((y-5)^2)/(4^2) = 1
a. Use the ezplot command to plot the two equations in the same figure. Plot must show
all real roots.
b. Using the plot, determine initial guesses for each of the real root of the system of non-
linear equations.
c. Evaluate each real root using Newton-Raphson Method.
The following are the requirement for parts d
1. All codes must use the following stopping criteria significant 0.5E(n-2) is reached for
both x and y. n = 8
Approximate Percent Relative Error x = |(xnew - xold)/(xnew)| × 100%$
Approximate Percent Relative Error y =|(ynew - yold)/(ynew)| ×100%$
2. Initial values of x and y must be entered by the user. (Hint: Use input command)
3. Display the results using fprintf for each root. Using
Newton-Raphson Method, the root is located at x = ### and y = ### after ##
iterations, yielding a relative percent error ###.
Submit file called nonlinearlastname in Blackoard before beginning of class.
Extra credit: Submit a flow chart for the code. Label file NFFlowchartlastname.pdf

Added by Robert Y.

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