Question

Evaluate and Interpret a condition number for the following:

f(x)=sqrt(abs(x-1))+1 for x=1.00001

f(x)=e^-x doe x=10

f(x)=sin(x)/(1+cos(x)) for x=1.0001*pi

USE MATLAB

Answer 1

clc;
clear all;
format short
f=@(x)sqrt(abs(x-1))+1; %function
df=@(x)1/(sqrt(x-1)*2); %derivative of function
x=1.00001;
f(x)
df(x)
% Condition number
disp('Condition number')
k=x*df(x)/f(x)

%%%%%%%%% Answer

ans =

1.0032

ans =

158.1139

Condition number

k =

157.6170

>>

2)

clc;
clear all;
format short
f=@(x)exp(-x); %function
df=@(x)-exp(-x); %derivative of function
x=10;
f(x)
df(x)
% Condition number
disp('Condition number')
k=x*df(x)/f(x)

%%%%%% Answer

ns =

4.5400e-05

ans =

-4.5400e-05

Condition number

k =

-10

>>

3)

clc;
clear all;
format short G
f=@(x)sin(x)/(1+cos(x)) ; %function
df=@(x)1/(cos(x)+1); %derivative of function
x=1.0001*pi;
f(x)
df(x)
% Condition number
disp('Condition number')
k=x*df(x)/f(x)
%%%%%%%%%%%%%%%% Answer

ans =

-6366.2

ans =

2.0264e+07

Condition number

k =

-10001

>>