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• Hint for problem 1: n=3 digits means that the mantissa is of the form (d₁.d₂d₃)₂. Assume that the machine uses only normalized machine numbers (d₁=1). For numbers between zero and the smallest positive machine number x_min you can either always round to 0, or round to the closest of the two numbers 0 and x_min.

  In (b), the machine number is (1.01)₂ 2¹.

• Hint for problem 2: Assume that the values for the exponents are set up analogously as explained for single precision numbers.
• Hint for problem 4: For (a) remember how I rearranged cos(x)-1 in class to avoid subtractive cancellation

  Part (b): For determining the condition number consider x₁ as a function f(b) depending on b (for fixed c).

• Hint for problem 5(b): Find an upper bound for the relative error, by using the results on error propagation and roundoff error from class.

Ass2

• Assignment #1 is due on Thu, Feb. 14
  Hint for 3(b)(c), 4(b)(c): To decide whether computation is numerically stable, compare the computed relative erros with unavoidable error from part (a) (do not analyze the algorithm step by step).