Compress and split large files

# create archives
$ tar cz my_large_file_1 my_large_file_2 | split -d -b 1024MiB - myfiles_split.tgz_

# uncompress
$ cat myfiles_split.tgz_* | tar xz

This solution avoids the need to use an intermediate large file when (de)compressing. Use the tar -C option to use a different directory for the resulting files. btw if the archive consists from only a single file, tar could be avoided and only gzip used:

# create archives
$ gzip -c my_large_file | split -d -b 1024MiB - myfile_split.gz_

# uncompress
$ cat myfile_split.gz_* | gunzip -c > my_large_file