Partial pivoting in the computation of Krylov subspaces of large sparse systems

The use of Krylov subspace approaches, based on the Arnoldi iteration, has become a preferred technique for the solution of several medium to high order matrix equations. These include linear algebraic systems of equations as well as Riccati, Lyapunov and Sylvester equations encountered in control systems. In this paper it is shown that existing implementations of Arnoldi iteration for computation of orthogonal basis of Krylov subspace can lead to erroneous conclusions. A partial pivoting strategy is proposed that overcomes the pitfall in implementations currently in use.