Abstract
In this paper, we propose several algorithms for computing the solutions of the following three problems: Problem I Given X, B ∈ C n × m ( n > m), find a centrohermitian matrix A ∈ C n × n such that ∥ AX − B∥ = min. Problem II Given X, B ∈ C n × m ( n > m), find a centrohermitian matrix A ∈ C n × n such that AX = B. Problem III Let S be the solution set of Problem I or Problem II. Given A ∼ ∈ C n × n , find A ∗ ∈ S such that | | A ∼ - A ∗ | | = inf A ∈ S | | A ∼ - A | | , where ∥ · ∥ is the Frobenius norm. We show that our algorithms ensure significant savings in computational costs, as compared to the case of an arbitrary matrix A.
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