% diary for Math 551 for 2/7/12
% see text page 40

format long
A=[17 5;1.7 0.5]

A =

  17.000000000000000   5.000000000000000
   1.700000000000000   0.500000000000000

b=[22;2.2]

b =

  22.000000000000000
   2.200000000000000

x_exact=[1;1]

x_exact =

     1
     1

A*x

ans =

  22.000000000000000
   2.200000000000000

x=A\b
Warning: Matrix is close to singular or badly scaled.
         Results may be inaccurate. RCOND = 3.265362e-018.

x =

  -1.058823529411765
   8.000000000000000

svd(A)

ans =

  17.808424972467385
                   0

format long e
mu=A(2,1)/A(1,1)

mu =

    9.999999999999999e-002

A(2,:)=A(2,:)-mu*A(1,:)

A =

    1.700000000000000e+001    5.000000000000000e+000
                         0    5.551115123125783e-017

b(2)=b(2)-mu*b(1)

b =

    2.200000000000000e+001
    4.440892098500626e-016

2*eps

ans =

    4.440892098500626e-016

x(2)=b(2)/A(2,2)

x =

   -1.058823529411765e+000
    8.000000000000000e+000

x(1)=(b(1)-A(1,2)*x(2))/A(1,1)

x =

   -1.058823529411765e+000
    8.000000000000000e+000

A*x

ans =

    2.200000000000000e+001
    4.440892098500626e-016

A_original=[17 5;1.7 0.5]

A_original =

    1.700000000000000e+001    5.000000000000000e+000
    1.700000000000000e+000    5.000000000000000e-001

A_original*x

ans =

    2.200000000000000e+001
    2.200000000000000e+000

A=[17.00001 5; 1.7 0.5]

A =

    1.700001000000000e+001    5.000000000000000e+000
    1.700000000000000e+000    5.000000000000000e-001

svd(A)

ans =

    1.780843451851116e+001
    2.807658357150557e-007

x_exact=[1;1]

x_exact =

     1
     1

b=A*x_exact

b =

    2.200001000000000e+001
    2.200000000000000e+000

x=A\b

x =

    9.999999996669331e-001
    1.000000001132428e+000

A=[17.1 5; 1.7 0.5]

A =

    1.710000000000000e+001    5.000000000000000e+000
    1.700000000000000e+000    5.000000000000000e-001

svd(A)

ans =

    1.790390996963804e+001
    2.792686071634185e-003

x_exact=[1;1]

x_exact =

     1
     1

b=A*x_exact

b =

    2.210000000000000e+001
    2.200000000000000e+000

x=A\b

x =

    9.999999999999946e-001
    1.000000000000019e+000

diary off