• Hints for Assignment 1:
  • problem 1(d): Use a=1 and b such that fl(1+b)=1.
  • problem 2: All questions are for double precision (this is what Matlab uses).
  • problem 3(a): We have x1 = f(c) where f(c) = ... - sqrt(... - ...). Use the condition number cond_f=c*f'(c)/f(c). Consider b as a fixed parameter. Then for (i), (ii), (iii) evaluate cond_f with b:=-x₁-x₂, c:=x₁x₂ in Matlab.
    problem 3(b): The file qeq1.m should look like this:
    function [x1,x2] = qeq1(b,c)
    x1 = ... ;
    x2 = ... ;
    To find the errors of your computed solution use
    x1 = ... ; x2 = ... ;
b = -x1-x2; c = x1*x2;
[x1hat, x2hat] = qeq1(b,c)
    and then compute the relative errors of x1hat, x2hat compared to x1, x2.
  • 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).