e-x + x = 0 i) Explain Newton's algorithm. (5p) ii) Write a computer code for...

 

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e-x + x = 0 i) Explain Newton's algorithm. (5p) ii) Write a computer code for Newton algorithm. (5p) iii) Calculate first three step of the Newton algorithm by hand to find positive root of the equation with initial point x = -2. (5p) iv) Use your computer code to find the root with error less than xn+1-Xnl = 10-7 for initial point x = -2. Obtain the table which contains n, xn, f(xn), f'(xn), xn+1, [xnXn+1l values for each iteration step. (5p) v) Repeat iv) by your secant code for initial points xo = -2, x = 0 to obtain the table which contains n, xn-1, Xn, Xn+1, xn+1 = xnl values for each iteration step. (5p) e-x + x = 0 i) Explain Newton's algorithm. (5p) ii) Write a computer code for Newton algorithm. (5p) iii) Calculate first three step of the Newton algorithm by hand to find positive root of the equation with initial point x = -2. (5p) iv) Use your computer code to find the root with error less than xn+1-Xnl = 10-7 for initial point x = -2. Obtain the table which contains n, xn, f(xn), f'(xn), xn+1, [xnXn+1l values for each iteration step. (5p) v) Repeat iv) by your secant code for initial points xo = -2, x = 0 to obtain the table which contains n, xn-1, Xn, Xn+1, xn+1 = xnl values for each iteration step. (5p)

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i Newtons algorithm also known as Newtons method or NewtonRaphson method is an iterative method for finding the roots of a function It is based on the concept of using successive linear approximations ... View the full answer