Volume 19, Issue 4
On the Estimations of Bounds for Determinant of Hadamard Product of H-Matices
DOI:

J. Comp. Math., 19 (2001), pp. 365-370

Published online: 2001-08

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• Abstract

In this paper, some estimations of bounds for determinant of Hadamard product of H-matrices are given. The main result is the following if A = (a_ij) and B=(b_ij) are nonsingular H-matrices of order n and \Sum^n_i=1 a_iib_ii › 0, and A_k and B_k, k=1, 2, \cdots, n, are the k \times k leading principal submatrices of A and B, respectively, then $$deet (A o B) \ge |a_11b_11| \Sum^n_k=2 [|b_kk| \frac{det M(A_k)}{det M(A_k-1)} + \frac{det M(B_k)}{M(B_k-1)} (\sum^{k-1}_{i=1}|\frac{a_ika_ki}{a_ii}|)],$$ where M(A_k) denotes the comparison matrix of A_k.

• Keywords

@Article{JCM-19-365, author = {}, title = {On the Estimations of Bounds for Determinant of Hadamard Product of H-Matices}, journal = {Journal of Computational Mathematics}, year = {2001}, volume = {19}, number = {4}, pages = {365--370}, abstract = { In this paper, some estimations of bounds for determinant of Hadamard product of H-matrices are given. The main result is the following if A = (a_ij) and B=(b_ij) are nonsingular H-matrices of order n and \Sum^n_i=1 a_iib_ii › 0, and A_k and B_k, k=1, 2, \cdots, n, are the k \times k leading principal submatrices of A and B, respectively, then $$deet (A o B) \ge |a_11b_11| \Sum^n_k=2 [|b_kk| \frac{det M(A_k)}{det M(A_k-1)} + \frac{det M(B_k)}{M(B_k-1)} (\sum^{k-1}_{i=1}|\frac{a_ika_ki}{a_ii}|)],$$ where M(A_k) denotes the comparison matrix of A_k. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8989.html} }
TY - JOUR T1 - On the Estimations of Bounds for Determinant of Hadamard Product of H-Matices JO - Journal of Computational Mathematics VL - 4 SP - 365 EP - 370 PY - 2001 DA - 2001/08 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8989.html KW - H-matrix KW - Determinant KW - Hadamard product AB - In this paper, some estimations of bounds for determinant of Hadamard product of H-matrices are given. The main result is the following if A = (a_ij) and B=(b_ij) are nonsingular H-matrices of order n and \Sum^n_i=1 a_iib_ii › 0, and A_k and B_k, k=1, 2, \cdots, n, are the k \times k leading principal submatrices of A and B, respectively, then $$deet (A o B) \ge |a_11b_11| \Sum^n_k=2 [|b_kk| \frac{det M(A_k)}{det M(A_k-1)} + \frac{det M(B_k)}{M(B_k-1)} (\sum^{k-1}_{i=1}|\frac{a_ika_ki}{a_ii}|)],$$ where M(A_k) denotes the comparison matrix of A_k.