1. Get a vector of initial guesses xo, the required accuracy and maximum number of steps....

  

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1. Get a vector of initial guesses xo, the required accuracy and maximum number of steps. Initialize current guess Xold = X0. 2. Evaluate the system functions F and the Jacobian function J at current guess xold. 3. Find new guess Xnew = Xold - J(Xold)-F(Xold). 4. If the Euclidean distance between Xnew and xold is less than the required accuracy, then stop and Xnew is the answer. 5. Otherwise, go back to Step 2 with Xold = Xnew. Repeat until maximum number of steps reached. Problem 8.3 Write the code for the above algorithm and include it in your solution. Problem 8.4 Run your code with accuracy as 0.01, maximum number of steps as 100 and initial guesses of your choice. Use d = 1.0, d = 1.0, Rdes = 1.0 and Hdes = 1.1. 1. What are the angles that Newton's method returns? Include your guess and the result in the Results section. Describe if it makes sense when seen within the range of motion surface plot. (Just saying "Yes" or "No" will not be given any credit.) 2. Find a value for the initial guess x0 that causes Newton's method to fail. What is your "bad" guess? How does this make sense? Write down a thorough reasoning. 1. Get a vector of initial guesses xo, the required accuracy and maximum number of steps. Initialize current guess Xold = X0. 2. Evaluate the system functions F and the Jacobian function J at current guess xold. 3. Find new guess Xnew = Xold - J(Xold)-F(Xold). 4. If the Euclidean distance between Xnew and xold is less than the required accuracy, then stop and Xnew is the answer. 5. Otherwise, go back to Step 2 with Xold = Xnew. Repeat until maximum number of steps reached. Problem 8.3 Write the code for the above algorithm and include it in your solution. Problem 8.4 Run your code with accuracy as 0.01, maximum number of steps as 100 and initial guesses of your choice. Use d = 1.0, d = 1.0, Rdes = 1.0 and Hdes = 1.1. 1. What are the angles that Newton's method returns? Include your guess and the result in the Results section. Describe if it makes sense when seen within the range of motion surface plot. (Just saying "Yes" or "No" will not be given any credit.) 2. Find a value for the initial guess x0 that causes Newton's method to fail. What is your "bad" guess? How does this make sense? Write down a thorough reasoning.