In computational mathematics, a matrix-free method is an algorithm for solving a linear system of equations or an eigenvalue problem that does not store the coefficient matrix explicitly, but accesses the matrix by evaluating matrix-vector products.
Many iterative methods allow for a matrix-free implementation, including: Distributed solutions have also been explored using coarse-grain parallel software systems to achieve homogeneous solutions of linear systems.
Matrix-free conjugate gradient method has been applied in the non-linear elasto-plastic finite element solver.
[7] Solving these equations requires the calculation of the Jacobian which is costly in terms of CPU time and storage.
Manipulating and calculating this vector is easier than working with a large matrix or linear system.