

Here are small examples of using ExLAF77: solution of system of equations
with Hilbert matrix and finding eigenvalues of Van der Monde matrix.
These applications come with Windows exe files so you can download and run them
without need to compile (see also important notes about these executables).
The user interface is intentionally made primitive
to keep the source uncluttered from code inessential for main purpose.
Hilbert matrix defined by formula H_{i,j}=1/(i+j1) is wellknown for its extremely
high condition number sharply increasing with matrix order (see the table below). This makes
inverting Hilbert matrix a challenge even at small n, if nativeprecision arithmetics is used.
Van der Monde matrices are also illconditioned starting from matrix
orders well under 10. Here we use Van der Monde matrices of the form
V_{i,j }=^{ }i^{ j1}
matrix order 
condition number of Hilbert matrix 
condition number (spectral) of Van der Monde matrix 
1  1.0  1.0 
10  1.6e+13  2.1e+12 
20  2.5e+28  1.8e+31 
30  4.2e+43  3.2e+52 
40  7.6e+58  1.7e+75 
50  1.4e+74  1.2e+99 
60  2.7e+89  6.5e+123 
70  5.2e+104  1.9e+149 
80  9.9e+119  2.3e+175 
90  1.9e+135  9.6e+201 
100  3.8e+150  1.2e+229 

This application will ask to enter matrix order n and the number of 4byte words
for mantisa and exponent. It is enough to set 1 word for exponent. As a reference point,
for the Hilbert matrix of n=100 you may wish to specify a mantissa of 30 words.
If precision (mantissa) is insufficient for given matrix order, an error message
is printed and application stops. You can easily modify it so that instead of exiting, it
automatically increases precision and starts over.
The righthand side vector is read from a plain text file that should be named "HILBERT_RHS.TXT".
For your convenience we provide a sample RHS input file. The program reads only as many
elements from it as the matrix order n you specify at program start. There is no need
to delete unnecessary values from the input file.
The solution vector will be printed into file HILBERT_SOL.TXT.

This application will ask to enter matrix order n and the number of 4byte words
for mantisa and exponent. It is enough to set 1 word for exponent. As a reference point,
for the Van der Monde matrix of n=100 you may wish to specify a mantissa of 50 words.
If precision (mantissa) is insufficient for given matrix order, an error message
is printed and application stops. As in the previous example, it is easy to make it
automatically start over with a higher precision.
The resulting eigen values are printed into text file "VANDERMONDE_EV.TXT".

Exe files provided on this page are intended only for Windows x86 platforms.
They require no installation and do not depend on other files (except for data input
as described above) nor on the directory where running.
We certify that demo
examples do not access your registry nor any other files and information on your
computer, except creating result file as described, and they do not send any
information over the net. In other words they do not perform any operations
except calculations described here.




