The work is devoted to algorithms for solving the inverse gravimetry problem of finding an interface between media from gravity data and the magnetometry problem for the case of an arbitrarily directed magnetization from magnetic data and their implementation on graphics processors. Based on the conjugate gradient method using the Toeplitz-block-Toeplitz structure of the matrix of integral operator derivatives, we construct the efficient modified algorithms for solving inverse gravimetry and magnetometry problems. A new componentwise method is elaborated for solving the inverse magnetometry problem for the case of an arbitrarily directed magnetization vector. Numerical experiments are carried out on the GPU to study the applicability and performance of the developed algorithms.