论文标题
部分可观测时空混沌系统的无模型预测
A skew-symmetric Lanczos bidiagonalization method for computing several largest eigenpairs of a large skew-symmetric matrix
论文作者
论文摘要
真正的偏斜矩阵$ a $的光谱分解可以数学地转换为$ a $的特定结构化奇异值分解（SVD）。 Based on such equivalence, a skew-symmetric Lanczos bidiagonalization (SSLBD) method is proposed for the specific SVD problem that computes extreme singular values and the corresponding singular vectors of $A$, from which the eigenpairs of $A$ corresponding to the extreme conjugate eigenvalues in magnitude are recovered pairwise in real arithmetic.建立了该方法的许多收敛结果，并给出了近似单数三重态的准确性估计。在有限的精度算术中，证明每组矢量的半正交性以及两组基础向量的半偏态性足以准确计算奇异值。一种常用的有效局部重新配合策略是适应所需的半正交性和半偏态性的。出于实际目的，隐式重新启动的SSLBD算法是通过部分重新定义开发的。数值实验说明了算法的有效性和总体效率。
The spectral decomposition of a real skew-symmetric matrix $A$ can be mathematically transformed into a specific structured singular value decomposition (SVD) of $A$. Based on such equivalence, a skew-symmetric Lanczos bidiagonalization (SSLBD) method is proposed for the specific SVD problem that computes extreme singular values and the corresponding singular vectors of $A$, from which the eigenpairs of $A$ corresponding to the extreme conjugate eigenvalues in magnitude are recovered pairwise in real arithmetic. A number of convergence results on the method are established, and accuracy estimates for approximate singular triplets are given. In finite precision arithmetic, it is proven that the semi-orthogonality of each set of basis vectors and the semi-biorthogonality of two sets of basis vectors suffice to compute the singular values accurately. A commonly used efficient partial reorthogonalization strategy is adapted to maintaining the needed semi-orthogonality and semi-biorthogonality. For a practical purpose, an implicitly restarted SSLBD algorithm is developed with partial reorthogonalization. Numerical experiments illustrate the effectiveness and overall efficiency of the algorithm.
