Estimates of the p-Norms of Solutions and Inverse Matrices of Systems of Linear Equations with a Circulant Matrix
Yu. S. Volkov, V. V. Bogdanov · Computational Mathematics and Mathematical Physics · 2024
The article considers the problem of estimating solutions and inverse matrices of systems of linear equations with a circulant matrix in the $$p$$ -norm, $$1 \leqslant p < \infty $$ . An estimate for a diagonally dominant circulant matrix is obtained. Based on this result and the idea of decomposing a matrix into a product of matrices associated with the decomposition of a characteristic polynomial, an estimate for the general circulant matrix is proposed.