A new algorithm for solving large inhomogeneous linear system of algebraic equations

An algorithm based on a small matrix approach to the solution of a system of inhomogeneous linear algebraic equations is developed and tested in this short communication. The solution is assumed to lie in an initial subspace and the dimension of the subspace is augmented iteratively by adding the component of the correction vector obtained from the Jacobi scheme on the coefficient matrix A (A^TA, if the matrix A is nondefinite) that is orthogonal to the subspace. If the dimension of the subspace becomes inconveniently large, the iterative scheme can be restarted. The scheme is applicable to both symmetric and nonsymmetric matrices. The small matrix is symmetric (nonsymmetric), if the coefficient matrix is symmetric (nonsymmetric). The scheme has rapid convergence even for large nonsymmetric sparse systems.