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
Abstract:
Formulas for inverting regularized systems of linear equations whose coefficient matrices are complex, Toeplitz, and singular or nearly singular are derived. They make it possible to develop economical algorithms for solving such systems in mass calculations.
Key words:matrices, Toeplitz matrices, matrix inversion, unstable systems of linear equations, regularization, circulants, skew-circulants, spectral decompositions, economical numerical algorithms.
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