论文标题
Hessenberg Matrix和Hessenberg-bidiagonal基质铅笔之间的同一光谱转换，而无需使用减法
An isospectral transformation between Hessenberg matrix and Hessenberg-bidiagonal matrix pencil without using subtraction
论文作者
论文摘要
我们使用正交多态度的理论来保存稀疏性，在保留稀疏性的同时，通过鞋面和下二亚角矩阵从广义特征值问题和下部bidiagonal矩阵引入了特征值的转化算法。该过程是在没有减法的情况下制定的，这会导致数值不稳定。此外，讨论了上biDiagonal矩阵是Hessenberg类型的扩展情况的算法。
We introduce an eigenvalue-preserving transformation algorithm from the generalized eigenvalue problem by matrix pencil of the upper and the lower bidiagonal matrices into a standard eigenvalue problem while preserving sparsity, using the theory of orthogonal polynomials. The procedure is formulated without subtraction, which causes numerical instability. Furthermore, the algorithm is discussed for the extended case where the upper bidiagonal matrix is of Hessenberg type.
