=== GNucap Linear Solver ===
Gnucal linear solver is implemented in file m_matrix.h - that is C++ template.

Most things are depicted in very extensive comments to this file.
Some things which are discovered and are listed here.

== No zero diagonal element allowed ==

Solver has an issue if diagonal element is zero. lets consider system:

<code>
  | eps   -1|        | -1 |
  |         | *X  =  |    |
  | 10   -10|        |  0 |  
</code>

if eps =0 or close to 0 (like 1.e-20 or so) current solver gives wrong answer of {1,0}.

having eps=1.e-6 answer id ok = {1,1}

This may be explained that during LU decomposition with no permutations with very small eps some values may grow higher 1/machine_eps and mask significant digits.

Practical advice: 
Do not use .options gmin smaller than 1.e-6 .. 1.e-8 unless you know what you do.
With current solver in my distort results .

Note - spice circuit which creates this system:
<code>
* circuit - close to Rozenbrok
.options nobypass
.options gmin = 1.e-6
* i1 = 10 *( v2 - v1^2)
* i2 = 1 - v1
* 
I1  1 0      dc 0
G11 1 0 1 0  -10
G11 1 0 2 0   10

G21 2 0 1 0   -1
I2  2 0      dc 1

.print op v(1) v(2) i(I1) i(I2)

.op
.end

</code>