报告人：魏益民 教授（复旦大学）

时间：2025年11月01日 10:00-

地址：数统学院LD718

摘要：In this paper, we propose a new randomized iterative algorithm RQI-SPCGTLS  (Rayleigh Quotient Iteration with Sketching Preconditioned Conjugate Gradient method for Total  Least Squares problems) for solving the large-scale overdetermined total least squares (TLS) problems. In order to reduce the cost of initial guess construction, we prove the effectiveness of a backward stable least squares (LS) solution and utilize the randomized solver for the LS problem. We derive a new explicit expression for the optimal backward error of a TLS system and relate it to the well-known result in the least squares setting. This work formally provides theoretical analysis on the feasibility of leveraging the LS information to solve the TLS problem. As to the PCG subroutine, we innovate by substituting the complete Cholesky factorization with the sketching preconditioner. We verify its effectiveness within the finite-precision arithmetic with respect to the reduced condition number and the preservation of the convergence rate. Numerical experiments show that the RQI-SPCGTLS beats the classic RQI-PCGTLS and its mixed precision variant, likely to be a stable solver when it is effective.

邀请人：李寒宇

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