To continue, just send the message, send index from netlib, in your email
text. Extract the programs from the email messages and compile them. To
use the subroutines, you will need first to write a main program which
defines the dimensions and calls the subroutines. Once the main program is
in place, factor the matrix **A** using * dgeco.f*. This program will
also estimate the condition number of the matrix. Using *
dgesl.f*,
solve a linear system, **Ax=b** using the matrix **A** given above and a right
hand side vector with each entry equal to . Save your answer. Now
change the first entry in the right hand side from to and solve
the system again. Try this for different sizes of **n**. Since this is a
linear system, small changes in the inputs should yield small changes in
the output. So what has happened? Use * dsvdc.f* on the matrix **A** and
calculate the singular values. Take the ratio of the maximum to minimum
singular value. This will give you another estimate of the condition number of
the matrix **A**. Compare this number with the one calculated by the program
* dgeco.f*. The condition number tells you how many bits of information
you can expect to lose during an inversion procedure. Given the condition
number you calculated, what precision can you expect in the solution?