GNU Octave, version 3.2.2
Copyright (C) 2009 John W. Eaton and others.
This is free software; see the source code for copying conditions.
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FITNESS FOR A PARTICULAR PURPOSE.  For details, type `warranty'.

Octave was configured for "i486-pc-linux-gnu".

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octave> A=[1.0000 1.0000; 1.0000 1.0001]
A =

   1.0000   1.0000
   1.0000   1.0001

octave> c=[2.0000;2.0000]
c =

   2
   2

octave> d=[2.0000;2.0001]
d =

   2.0000
   2.0001

octave> x1=A\c
x1 =

   2
   0

octave> x2=A\d
x2 =

   1.00000
   1.00000

octave> norm(c-d,inf)/norm(c,inf)
ans =  5.0000e-05
octave> cond(A,inf)
ans =  4.0004e+04
octave> cond(A,inf)* norm(c-d,inf)/norm(c,inf)
ans =  2.0002
octave> norm(x1-x2,inf)/norm(x1,inf)
ans =  0.50000
octave> B=[1.0000 1.0000; 1.0000 0.0001]
B =

   1.0000e+00   1.0000e+00
   1.0000e+00   1.0000e-04

octave> x3=B\c
x3 =

   2
  -0

octave> x4=B\d
x4 =

   2.0001e+00
  -1.0001e-04

octave> cond(B,inf)
ans =  4.0004
octave> cond(B,inf)*norm(c-d,inf)/norm(c,inf)
ans =  2.0002e-04
octave> norm(x3-x4,inf)/norm(x3,inf)
ans =  5.0005e-05
