Abstract
At first, recall Krylov subspace which generated by matrix A and vector v. And then introduce a kid of procedure for solving quadratic eigenvalue problem (QEP) which is called RSTO procedure. Because of the structure preserving of RSTO procedure, hence, RSTO procedure can be naturally reduce quadratic eigenvalue problem (QEP) to linear eigenvalue problem, for help us to solve large-scale matrix problems. Finally, given some example compare with RSTO, Arnoldi and Second order Arnoldi method (SOAR) procedure for computational cost, orthogonality and uniqueness.