A note on estimates of diagonal elements of the inverse of diagonally dominant tridiagonal matrices.

Politi, Tiziano; Popolizio, Marina

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In this paper, we mainly use the properties of the minimum eigenvalue of the Fan product of $M$ -matrices and Cauchy-Schwarz inequality, and propose some new bounds for the minimum eigenvalue of the Fan product of two $M$ -matrices. These results involve the maximum absolute value of off-diagonal entries of each row. Hence, the lower bounds for the minimum eigenvalue are easily calculated in the practical examples. In theory, a comparison is given in this paper. Finally, to illustrate our...