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Samar, Mahvish; Zhu, Xinzhong; Xu, Huiying
Axioms, 06/2024, Letnik: 13, Številka: 6Journal Article
The conditioning theory of the ML-weighted least squares and ML-weighted pseudoinverse problems is explored in this article. We begin by introducing three types of condition numbers for the ML-weighted pseudoinverse problem: normwise, mixed, and componentwise, along with their explicit expressions. Utilizing the derivative of the ML-weighted pseudoinverse problem, we then provide explicit condition number expressions for the solution of the ML-weighted least squares problem. To ensure reliable estimation of these condition numbers, we employ the small-sample statistical condition estimation method for all three algorithms. The article concludes with numerical examples that highlight the results obtained.
