  We propose the sparse modeling approach for quasiclassical theory of
superconductivity, which reduces the computational cost of solving the gap
equations. The recently proposed sparse modeling approach is based on the fact
that the Green's function has less information than its spectral function and
hence is compressible without loss of relevant information. With the use of the
so-called intermediate representation of the Green's function in the sparse
modeling approach, one can solve the gap equation with only 10-100 sampled
Matsubara Green's functions, while the conventional quasiclassical theory needs
100-1000 ones. We show the efficiency of our method in bulk and vortex states,
by self-consistently solving the Eilenberger equations and gap equations. We
claim that the sparse modeling approach is appropriate in all theoretical
methods based on the Matsubara formalism in the quasiclassical theory of
superconductivity.
