报告题目：A generalized skew-symmetric Lanczos bidiagonalization method for computing several extreme eigenpairs of a large skew-symmetric/symmetric positive definite matrix pair

报告人：黄金枝 副教授 （清华大学）

报告时间：2026年5月29日（星期五） 16:00-17:00

报告地点：6776永利集团111A（党建活动室）

校内联系人：董波 教授  联系方式：84708351-8211

报告摘要：: A generalized skew-symmetric Lanczos bidiagonalization (GSSLBD) method is proposed to compute several extreme eigenpairs of a large matrix pair (A, B), where A is skew-symmetric and B is symmetric positive definite. The underlying GSSLBD process produces two sets of B-orthonormal generalized Lanczos basis vectors that are also B-biorthogonal and a sequence of bidiagonal matrices whose singular val¬ues are taken as the approximations to the imaginary parts of certain eigenvalues of (A, B) and the corresponding left and right singular vectors premultiplied by the left and right generalized Lanczos basis matrices form the real and imaginary parts of the associated approximate eigenvectors. A rigorous convergence analysis is made on the distance of the desired eigenspace and the Krylov subspaces generated by the GSSLBD process, and accuracy estimates are obtained for the approximate eigenpairs. In finite precision arithmetic, it is shown that the semi-B-orthogonality and semi-B-biorthogonality of the computed left and right generalized Lanczos vectors suffice to compute the eigenvalues accurately. An efficient partial reor¬thogonalization strategy is designed for GSSLBD in order to maintain the desired semi-B-orthogonality and semi-B-biorthogonality. GSSLBD with practical inexact inner iterations is developed for the matrix pair (A, B) that uses the preconditioned conjugate gradient (PCG) method to inaccurately solve the linear equations with the coefficient matrix B. To be practical, an implicitly restarted GSSLBD algorithm is developed with partial B-reorthogonalization. Numerical experiments illustrate the robustness and overall efficiency of the implicitly restarted GSSLBD algorithm.

报告人简介：黄金枝，2015、2020年分别获得清华大学学士、博士学位，师从贾仲孝教授，现就职于苏州大学6776永利集团，任副教授。主要从事数值线性代数与大规模科学计算研究，聚焦于大规模代数特征值问题、奇异值分解与广义奇异值分解问题等的数值求解和高性能算法研究。在SIAM J. Sci. Comput., SIAM J. Matrix Anal. Appl., J. Sci. Comput., Numer. Algorithms上发表学术论文多篇。