Matrices of small Toeplitz rank, certain representations of the solution to an unstable system of linear equations with Toeplitz coefficient matrices, and related fast algorithms for solving such systems
The Toeplitz (cs)- and (sc)-decompositions are introduced and analysed for an arbitary square complex matrix based on their connections with solutions of two implicit Sylvester equations. Then, formulas for the solution of Tikhonov regularization problems are derived. These formulas show that the number of arithmetic operations required for solving a sequence of unstable problems is twice as large as the corresponding number for stable problems.
scientific article; zbMATH DE number 6505321