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# solution+to+HW3 - Solution to HW3 EGM3344 FALL 2010 Problem...

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Solution to HW3 EGM3344 FALL 2010 Problem 4.1 Problem 4.3 function ep = macheps % determines the machine epsilon e = 1; while (1) if e+1<=1, break, end e = e/2; end ep = 2*e; >> macheps ans = 2.2204e-016 >> eps ans = 2.2204e-016 Problem 4.4 function s = small % determines the smallest number sm = 1; while (1) s=sm/2; if s==0,break,end sm = s; end s = sm; This function can be run to give >> s=small s = 4.9407e-324 This result differs from the one obtained with the built-in realmin function, >> s=realmin

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s = 2.2251e-308 Problem 4.7 The true value can be computed as Using 3-digits with chopping This represents a percent relative error of Problem 4.12 The true value is f (3) = 554. zero order: first order: second order:
third order: Because we are working with a third-order polynomial, the error is zero. This is due to the fact that cubics have zero fourth and higher derivatives. Problem 4.15 The first derivative of the function at x = 2 can be evaluated as The points needed to form the finite divided differences can be computed as

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solution+to+HW3 - Solution to HW3 EGM3344 FALL 2010 Problem...

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