Estimating close approach between all asteroids themselves I am currently writing a C++ program to show asteroids in 3D, and find close approaches or collisions. I got my orbital elements from JPL https://ssd.jpl.nasa.gov/sbdb_query.cgi. So far so good, with over a million asteroids drawn in 5ms with my old Quadro GPU
But the problem is the variation of the elements over time. For example, CERES:
epoch,a,e,i,om,w,ma 
2459200.5,2.766089105818,.07816842657453,10.58789954719,80.27235841368,73.72488984426,205.5454154582
2459310.5,2.765760313090,.07831877879848,10.58807660401,80.26860808947,73.73699886586,229.1146825391

After only 4 months, the eccentricity and all other elements have changed as seen on the second line.
How can I compute the change in the parameters without knowing their derivatives?
Or where to get those derivatives?
I searched all JPL small bodies site and their telnet access or email, but could not find a way to download orbital elements with derivatives or a way to compute the change.
I am aware that the difference might be just a pixel on the screen but it represents hundreds of thousands of kilometres. What I want to do is study the close approach between the asteroids themselves and eventually near collision. I already did that for artificial satellites using SGP4 propagator using OpenCL running on GPU video card. I can propagate 20,000 satellites (include debris) in a few milliseconds and get results exact to 1 kilometre. Compare with Celestrak Socrate. A prediction of a 1,000-kilometre approach must be possible.
Does anybody know how?
Thanks folks for helping.
I knew about SPK files but from Horizon's telnet inteface there is a limit of 200 bodies per request.
Making over 5000 request might be possible but not very productive.
I also looked at the  DE421 file from ftp://ssd.jpl.nasa.gov/pub/eph/planets/bsp/ but it looks like the corrections for the 8+1 planets
here is the output from BRIEF, a SPICE utility: https://naif.jpl.nasa.gov/naif/utilities.html
BRIEF -- Version 4.0.0, September 8, 2010 -- Toolkit Version N0066
Summary for: de421.bsp
Bodies: MERCURY BARYCENTER (1)  SATURN BARYCENTER (6)   MERCURY (199)
    VENUS BARYCENTER (2)    URANUS BARYCENTER (7)   VENUS (299)
    EARTH BARYCENTER (3)    NEPTUNE BARYCENTER (8)  MOON (301)
    MARS BARYCENTER (4)     PLUTO BARYCENTER (9)    EARTH (399)
    JUPITER BARYCENTER (5)  SUN (10)                MARS (499)
    Start of Interval (ET)              End of Interval (ET)
    -----------------------------       -----------------------------
    1899 JUL 29 00:00:00.000            2053 OCT 09 00:00:00.000

I can always do a statistical estimate, any close approach being false but the overall count being close to reality.
Too bad to drop the project, I was getting nices pictures from it. The coloring is done against eccentricity, red=0