Roundoff Error Analysis of an Algorithm Based on Householder Bidiagonalization for Total Least Squares Problems

Zhanshan Yang and Xilan Liu
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Zhanshan Yang: School of Mathematics and Statistics, Qinghai Nationalities University, Xining 810007, China
Xilan Liu: School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji 721000, China

Mathematics, 2021, vol. 9, issue 20, 1-14

Abstract: For large-scale problems, how to establish an algorithm with high accuracy and stability is particularly important. In this paper, the Householder bidiagonalization total least squares (HBITLS) algorithm and nonlinear iterative partial least squares for total least squares (NIPALS-TLS) algorithm were established, by which the same approximate TLS solutions was obtained. In addition, the propagation of the roundoff error for the process of the HBITLS algorithm was analyzed, and the mixed forward-backward stability of these two algorithms was proved. Furthermore, an upper bound of roundoff error was derived, which presents a more detailed and clearer approximation of the computed solution.

Keywords: Householder bidiagonalization; NIPALS; roundoff error; total least squares problems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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