A note on condition numbers for generalized inverse CA and their statistical estimation
Abstract
In this paper, we consider the condition number for the generalized inverse CA. We first present the explicit expression of normwise mixed and componentwise condition numbers. Then, we derive the explicit expression of normwise condition number without Kronecker product using the classical method for condition numbers. With the intermediate result, i.e., the derivative of CA, we can recover the explicit expressions of condition numbers for solution of Indefinite least squares problem with equality constraint. To estimate these condition numbers with high reliability, we choose the probabilistic spectral norm estimator and the small-sample statistical condition estimation method and devise three algorithms. Numerical experiments are provided to illustrate the obtained results
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