Lecture on Numerical Linear Algebra by Dr. Huaian Diao: "Small Sample Statistical Condition Estimation for the Total Least Squares Problem"
January 23rd (Tuesday)
National Institute of Informatics
Small Sample Statistical Condition Estimation for the Total Least Squares Problem
Dr. Huaian DIAO
School of Mathematics and Statistics Northeast Normal University Changchun, China
In this talk, under the genericity condition, we propose the condition estimation of the total least squares (TLS) problem based on small sample condition estimation (SCE), which can be incorporated into the direct solver for the TLS problem via the singular value decomposition (SVD) of the augmented matrix [A, b]. Our proposed condition estimation algorithms are efficient for the small and medium size TLS problem because they utilize the computed SVD of [A, b] during the numerical solution to the TLS problem. Numerical examples illustrate the reliability of the algorithms. Both norm-wise and component-wise perturbations are considered. Moreover, structured condition estimations are investigated for the structured TLS problem. This is the joint work with Prof. Yimin Wei and Dr. Pengpeng Xie.
Ken Hayami (hayami(at)nii.ac.jp)