Convert giant TIFF to GIF

I'm going crazy trying to convert a 117MB TIFF to a smaller GIF on
linux.  I've tried "convert", which runs out of memory and dies, and
tif2gif, which core dumps.   Any other linux suggestions?

The source image is from NASA, "Blue Marble", 21600 x 10800, <http://
veimages.gsfc.nasa.gov/2433/land_shallow_topo_21600.tif> and I need it
converted to 4320 x 2160 GIF, and also 10800 x 5400 GIF.

Any ideas or help gratefully accepted!

--ian