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HW1 - Fall 2011 CMPSC/MATH 451 Homework Assignment#1 Due...

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Fall 2011, CMPSC/MATH 451 Homework Assignment #1 Due September 9 (hand over in class or submit via Angel by 11 am) 1 The Euclidean norm of an n -dimensional vector x is defined by || x || 2 = (Σ n i =1 x 2 i ) 1 / 2 . ( a ) Discuss how there may be overflow and harmful underflow in this computation when using floating-point arithmetic. ( b ) Write two functions for computing the norm, a straightforward one (square each element of vec- tor, accumulate partial sum using a loop), and a robust function (how would you avoid/reduce overflow and underflow errors in this case? Recall what we had seen in class about associativity of floating-point addition). ( c ) Devise an input vector (say, with 5 elements) that produces significantly different results using these two routines. Compare with the output using MATLAB/Octave’s norm function. List the MATLAB/Octave code, the test input vector, as well as the output on executing the functions with these inputs.
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  • Spring '08
  • staff
  • Euclidean space, input vector, Matlab/Octave code, significantly different results, test input vector, algebraically equivalent terms

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