News

• Assignment 1 is due on Monday, Feb. 28. You can either hand it in in class, or you can slide it later that day under the door of Dr. Osborn's office MTH 3108. Do not slide it under the door of my office!
• Hints for Assignment 1

  Problem 1: The machine numbers are of the form ±(. d₁ d₂ d₃ d₄)₂ · 2^e

  Problem 4: Typo: change .9998 to .09998 (IMPORTANT!)

  Problem 2(a),(b): Even when you use format long g, different machine numbers are sometimes displayed in the same way. E.g., x = 1 + 1e-15 is displayed as 1, but num2bin(x) or x-1 show that it is a different machine number.

  Problem 2(c): Typo: there should be a subscript 2, (...)₂

  Problems 3 and 4: In parts (b), (c) you don't have to analyze the error propagation step by step as I did in class. Use the unavoidable errors and the errors of your Matlab computations.

  Be careful to do all computations in Matlab (computation of b, t, solutions x₁, x₂, relative errors) so that full machine precision is used all the time. Store intermediate results in variables when you need to use them again. Do not copy the digits of some previous results, since the printed output of Matlab (even with format long g) does not represent full machine accuracy (see remark to Problem 2 above).

  Problem 4 (b), (c): In Matlab, compute the solutions x₁, x₂ step by step as in Gaussian elimination without pivoting (first compute multiplier, modified matrix element, modified element of rhs vector, then x₂, then x₁). For (c), first interchange the order of the equations, then proceed in the same way.