One of the most important, most difficult, and most exasperating unsolved problems of operator theory is the problem of invariant subspaces . 算子理論中最重要、最困難也最令人煩惱的未解決問題之一就是不變子空間問題。
The cheapest way to get one is to invoke the spectral theorem and to conclude that normal operators always have non-trivial invariant subspaces . 取得這樣結果的最省力的嘗試是引用光譜定理而得到正規算子恒有非平凡不變子空間的結論。
In the third chapter , the perturbation of invariant subspace , singular subspaces and deflating subspaces are discussed 第三章討論了不變子空間、奇異子空間對和收縮子空間對的擾動。
In this paper , we discuss a new class of m - paranormal operators and give the properties of these operators . further , we also give an existence condition of the invariant subspace 討論了一個新的算子類: m -仿正規算子.給出了這一類算子的部分性質及不變子空間存在的條件
Numerical result shows that the new method is more efficient in convergence than the standard lanczos algorithm ; the second algorithm generalizes the implicitly restarted arnoldi ( ira ) augmented by soreesen to the implicitly restarted lanczos algorithm , which improves the convergence rate of lanczos algorithm by making good use of the spectral information obtained from the previous process . the last algorithm utilizes deflation strategies to the second algorithm to forming invariant subspace for a , so that the stability can be kept in computing process 數值試驗表明,該算法比標準lanczos方法具有更好的收斂性;第二種算法是將求解特征值問題的隱式循環arnoldi方法( ira )應用于求解對稱不定線性方程組的lanczos算法,充分利用lanczos算法過程中的譜信息,確定預處理;第三種算法是在第二種算法的基礎上,運用收縮技巧,形成近似不變子空間,以提高收斂速度和數值穩定性。