Abstract:
The article considers the problem of estimating solutions and inverse matrices of systems of linear equations with a circulant matrix in the $p$-norm, $1\le p<\infty$. 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.
Key words:difference equation, circulant matrix, diagonal dominance, norm of the inverse matrix, solution estimate
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