Minimal residual method

A comparison of the norm of error and residual in the CG method (blue) and the MINRES method (green). The matrix used comes from a 2D boundary-value problem.

The Minimal Residual Method or MINRES is a Krylov subspace method for the iterative solution of symmetric linear equation systems. It was proposed by mathematicians Christopher Conway Paige and Michael Alan Saunders in 1975.[1]

In contrast to the popular CG method, the MINRES method does not assume that the matrix is positive definite, only the symmetry of the matrix is mandatory.

  1. ^ Christopher C. Paige, Michael A. Saunders (1975). "Solution of sparse indefinite systems of linear equations". SIAM Journal on Numerical Analysis. 12 (4): 617–629. doi:10.1137/0712047.