Harrod, W. J. LU-decompositions of tridiagonal irreducible H-matrices. (English) Zbl 0595.65028 SIAM J. Algebraic Discrete Methods 7, 180-187 (1986). The LU-decomposition of tridiagonal irreducible H-matrices is analyzed and bounds for the growth factor in the LU-decomposition are given. Reviewer: V.Mehrmann Cited in 2 Documents MSC: 65F05 Direct numerical methods for linear systems and matrix inversion 15A23 Factorization of matrices 15B48 Positive matrices and their generalizations; cones of matrices Keywords:M-matrices; Toeplitz matrices; LU-decomposition; tridiagonal irreducible H-matrices; bounds for the growth factor PDF BibTeX XML Cite \textit{W. J. Harrod}, SIAM J. Algebraic Discrete Methods 7, 180--187 (1986; Zbl 0595.65028) Full Text: DOI OpenURL References: [1] Berman, A.; Plemmons, R., Nonnegative matrices in the mathematical sciences, (1979) · Zbl 0484.15016 [2] Carlson, David, Controllability, inertia, and stability for tridiagonal matrices, Linear Algebra Appl., 56, 207, (1984) · Zbl 0531.15008 [3] Carlson, D.; Datta, B.; Johnson, C., A semidefinite Lyapunov theorem and the characterization of tridiagonal D-stable matrices, SIAM J. Algebraic Discrete Methods, 3, 293, (1982) · Zbl 0541.15008 [4] Fiedler, Miroslav; Pták, Vlastimil, On matrices with non-positive off-diagonal elements and positive principal minors, Czechoslovak Math. J., 12 (87), 382, (1962) · Zbl 0131.24806 [5] Funderlic, R.; Mankin, J., Solution of homogeneous systems of linear equations arising from compartmental models, SIAM J. Sci. Statist. Comput., 2, 375, (1981) · Zbl 0468.65042 [6] Funderlic, R.; Neumann, M.; Plemmons, R., \(LU\) decompositions of generalized diagonally dominant matrices, Numer. Math., 40, 57, (1982) · Zbl 0481.65017 [7] Funderlic, R.; Plemmons, R., \(LU\) decomposition of M-matrices by elimination without pivoting, Linear Algebra Appl., 41, 99, (1981) · Zbl 0473.65011 [8] Gunzburger, M.; Nicolaides, R., Stability of Gaussian elimination without pivoting on tridiagonal Toeplitz matrices, Linear Algebra Appl., 45, 21, (1982) · Zbl 0486.65019 [9] Inman, I., Tridiagonal and upper triangular inverse M-matrices, Linear Algebra Appl., 55, 93, (1983) · Zbl 0519.15009 [10] Wilkinson, J., Error analysis of direct methods of matrix inversion, J. Assoc. Comput. Mach., 8, 281, (1961) · Zbl 0109.09005 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.