• Assignment 1 is due Mon, Sept. 20. For the m-files num2bin.m and num2bin.m see "IEEE 754 double precision machine numbers in Matlab"
  Hints:
  • problem 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).
    problem 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
    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.
  • problem 4(b):To find the relative error of ytilde:=y1hat-xhat use
    |_ahat-bhat| <= |a/(a-b)| |_ahat | + |b/(a-b)| |_bhat |.
    problem 4(c): Use the remainder term to get an upper bound for |f(x)-f₄(x)|/|f(x)|.
    problem 4(d): linspace(a,b,n) gives n equidistant numbers in the interval [a,b] (including the endpoints).