Gauss-Newton Method for Nonlinear Least Squares Write a MATLAB program which, given a system of nonlinear functions and an initial set of values, will compute the least squares solution of f(x)-0 for f: Rn ? Rm using the Gauss-Newton Method numerically without second derivatives. 1. The main program should include x + a-x+/-t(Df(x))T(Df(x))T [(Df(x)'f(x)]}?x. For switching from 3(a) to 3(b), the main program should remain unchanged The first subroutine function gives the initial value x and the stop condition ? . The 2. second subroutine function uses x as the input and f(x), Df (x) as the output. The second subroutine is used several times depending on the number of iterations. 3. Test your program on the following two problems (a) (n = 3 , m = 7) Nonlinear least square exponential fit y = xtx-ery for the data points (1,y)= (1,53.05), (6.73.04), (11,98.31), (16,139.78), (21, 193.48), (26, 260.20) and (31, 320.39). The stopping condition is lal2 :-10-4and the initial value x (-0.1, 0.1) At the beginning of the program, write format long to claim more digits in the printout. Print out and hand in the program and the numerical results of x and ninax = norrn(ax) for each iteration of each problem. 4. Gauss-Newton Method for Nonlinear Least Squares Write a MATLAB program which, given a system of nonlinear functions and an initial set of values, will compute the least squares solution of f(x)-0 for f: Rn ? Rm using the Gauss-Newton Method numerically without second derivatives. 1. The main program should include x + a-x+/-t(Df(x))T(Df(x))T [(Df(x)'f(x)]}?x. For switching from 3(a) to 3(b), the main program should remain unchanged The first subroutine function gives the initial value x and the stop condition ? . The 2. second subroutine function uses x as the input and f(x), Df (x) as the output. The second subroutine is used several times depending on the number of iterations. 3. Test your program on the following two problems (a) (n = 3 , m = 7) Nonlinear least square exponential fit y = xtx-ery for the data points (1,y)= (1,53.05), (6.73.04), (11,98.31), (16,139.78), (21, 193.48), (26, 260.20) and (31, 320.39). The stopping condition is lal2 :-10-4and the initial value x (-0.1, 0.1) At the beginning of the program, write format long to claim more digits in the printout. Print out and hand in the program and the numerical results of x and ninax = norrn(ax) for each iteration of each problem. 4