首先回顧由一個矩陣和一個向量所生成Krylov子空間, 然後介紹一種解二次特徵值問題的方法稱之為RSTO演算法. 由於RSTO演算法的保結構性, 因此可以很自然的把二次特徵值問題轉換成線性的特徵值問題. 最後舉例比較RSTO, Arnoldi和SOAR演算法.

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.

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