Structured condition numbers for a linear function of the solution of the generalized saddle point problem

This paper addresses structured normwise, mixed, and componentwise condition numbers (CNs) for a linear function of the solution to the generalized saddle point problem (GSPP). We present a general framework enabling us to measure the structured CNs of the individual solution components and derive their explicit formulae when the input matrices have symmetric, Toeplitz, or some general linear structures. In addition, compact formulae for the unstructured CNs are obtained, which recover previous results on CNs for GSPPs for specific choices of the linear function. Furthermore, an application of the derived structured CNs is provided to determine the structured CNs for the weighted Teoplitz regularized least-squares problems and Tikhonov regularization problems, which retrieves some previous studies in the literature.