• Assignment 1: due date extended to Tue, Feb 14. . Please read How to Hand in Matlab Homework.

  Problem 1

  "Normalized" means that d₁=1.
  1(d): Try a=1 and very small values for b,c

  Problem 2

  Download the files num2bin.m (UPDATED) and bin2num.m (note that you have to put the files where Matlab can find them). Read IEEE 754 double precision machine numbers in Matlab.
  Note: Even with format long g, different machine numbers are sometimes displayed in the same way. E.g., x = 1 + 1e-15 is displayed as 1, but typing num2bin(x) or x-1 shows that it is a different machine number from 1.

  Problem 3

  3(a): f(c) = (-b - sqrt(b² - 4c))/2. Find a formula for c_f = c f'(c)/f(c). Evaluate this formula in Matlab for b = -y1-y2, c = y1*y2 where y1,y2 are the values in (i),(ii),(iii).
  3(b): The file qeq1.m should look like this:
  function [y1,y2] = qeq1(b,c)
  y1 = ... ;
  y2 = ... ;
  To find the errors of your computed solution use in your main code
  y1 = ... ; y2 = ... ;
b = -y1-y2; c = y1*y2;
[y1hat, y2hat] = qeq1(b,c)
  and then compute the relative errors of y1hat, y2hat compared to y1, y2.
  VERY IMPORTANT: Compute b, c from y1 and y2 in Matlab as shown above, in order to get full machine accuracy.
  3(b),(c): Just comment on the numerical stabilty of the results for y₁ only (not for y₂), since we know from (a) the unavoidable error for y₁.

  Problem 4

  4(b):To find the relative error of ytilde:=y1hat-xhat use
  |_ahat-bhat| <= |a/(a-b)| |_ahat | + |b/(a-b)| |_bhat |.
  4(c): Use the remainder term of the Taylor series to get an upper bound for |f(x)-f₄(x)|/|f(x)|.
  4(d): linspace(a,b,n) gives n equidistant numbers in the interval [a,b] (including the endpoints).