subroutine kvtx_unknown_approx(ntrk, list, vtx)
*
* begin_doc
*
*  Find 3-D vertex for several tracks using a straight line approximation. This
*  routine is used as a first step in a more accurate procedure.
*
*  Input Parameters:
*  ntrk        integer variable
*              Number of tracks
*
*  list        integer array
*              List of tracks in track list to use
*
*  Output Parameters:
*  vtx(3)      double precision array
*              (x,y,z) intersection point. If it cannot be determined, it is
*              set to (0,0,0).
*
*  Other routines:
*
*  Notes:
*
*  Author:   Paul R Avery      Created:  Mon Jul 28 06:55:56 EDT 1997
*
*  Major revisions:
*
*
C  >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
C  The lines are defined by the equation
C
C                  x = x0 + eta*r
C
C  where r is a free parameter (length) and eta is a set of direction
C  cosines. The track parametrization is the noncanonical one, i.e. x0, y0,
C  z0, nx, ny, nz, rho, p, Q, s. The curvature rho is ignored.
C
C  The intersection is defined as the point which minimizes the sum of
C  distances**2 to each of the lines:
C
C          d**2 = SUM(i) [ (x-x0(i)**2 - |(x-x0(i))*eta(i)|**2 ]
C
C  The sum is minimized when the x(j) components satisfy
C
C          0 = SUM(i) [ x(j)-x0(ij) - eta(ij)|(x-x0(i))*eta(i)| ]
C
C  These equations can be rewritten as a single matrix equation
C
C                 Ax = b
C
C                  x = A(inv) * b
C
C       | N-SUM[eta(i1)**2]    -SUM[eta(i1)eta(i2)]  -SUM[eta(i1)eta(i3)]|
C   A = |-SUM[eta(i1)eta(i2)]   N-SUM[eta(i2)**2)]   -SUM[eta(i2)eta(i3)]|
C       |-SUM[eta(i1)eta(i3)]  -SUM[eta(i2)eta(i3)]   N-SUM[eta(i3)**2]  |
C
C
C       |  SUM[x0(i1) - eta(i1)|x0(i)*(eta(i)| ]  |
C   b=  |  SUM[x0(i2) - eta(i2)|x0(i)*(eta(i)| ]  |
C       |  SUM[x0(i3) - eta(i3)|x0(i)*(eta(i)| ]  |
C
C
C   Dot product multiplication is indicated above by a *
C  >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
* end_doc