数学科学系

Department of Mathematical Sciences

Statistical Condition Estimates and Randomized Algorithms for Large-Scale Total Least Squares Problems

报告题目: Statistical Condition Estimates and Randomized Algorithms for Large-Scale Total Least Squares Problems

 

报告人:魏益民教授(复旦大学)

 

时间:2014911日(星期四)1500-1600

 

地点:理科楼数学系A404

 

摘要: In this talk, we present new perturbation analysis and randomized algorithms for the total least squares (TlS) problem. Our new perturbation results are sharper than the earlier ones. We prove that the condition numbers obtained by Zhou et al. [Numer. Algorithm, 51 (2009), pp. 381-399], Barboulin and Gratton [SIAM J. Matrix Anal. Appl., 32 (2011), pp. 685-699], Li and Jia [Linear Algebra Appl., 435 (2011), pp. 674-686] are mathematically equivalent. Statistical condition estimates (Sce) are applied to the TLS problem. Motivated by the recently popular probabilistic algorithms for low-rank approximations, we develop randomized algorithms for the TlS and the truncated total least squares (TlS) solutions of large-scale discrete ill-posed problems, which can greatly reduce the computational time and still keep good accuracy. Its efficiency is well demonstrated by numerical examples.

 

联系人:贾仲孝