f77 my_program.f -ldxml
(plus any other compiler options you might need) should do the job.
Notice that if the result of your computation is a matrix, then you have transform this result again.
Because of a difference in how names of subroutines are handled internally, you have to add an underscore (_) to all the routine names. Instead of,
sgesv(&c1, &c2, NEW, &c1, pivot, b, &c1, &ok);
it has to be,
sgesv_(&c1, &c2, NEW, &c1, pivot, b, &c1, &ok);
After that you can just say,
cc my_program.c -ldxml
(plus any other compiler options you might need) to compile your program.
The AIX operating system contains a library of basic linear algebra routines (blas) which LAPACK is based on but you have install LAPACK yourself (or find a nice system administrator to do it for you).
f77 my_program.f -llapack -lblas
(plus any other compiler options you might need) should do the job.
Notice that if the result of your computation is a matrix, then you have transform this result again.
After that you can just say,
cc my_program.c -llapack -lblas -lm -lxlf
(plus any other compiler options you might need) to compile your program.