Generalized Schur-complements and a test for total positivity

DOI10.1016/0168-9274(87)90049-3zbMath0621.65013OpenAlexW1987955213WikidataQ127352401 ScholiaQ127352401MaRDI QIDQ1090060

Günter W. Mühlbach, Mariano Gasca

Publication date: 1987

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-9274(87)90049-3

zbMATH Keywords

Gauss eliminationtotally positive matricesNeville eliminationdeterminantal identitiesSchur-complements

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) Miscellaneous inequalities involving matrices (15A45) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items

Trees, forests, and total positivity. I: \(q\)-trees and \(q\)-forests matrices ⋮ Pseudo-Schur complements and their properties ⋮ Block idempotent matrices and generalized Schur complement ⋮ Generalized Schur-complements and a test for total positivity ⋮ Some Schur complement identities and applications to matrix extrapolation methods ⋮ New vector sequence transformations ⋮ Linear extrapolation by rational functions, exponentials and logarithmic functions ⋮ Matrix extrapolation algorithms ⋮ Other manifestations of the Schur complement ⋮ The work of Mariano Gasca ⋮ On extending determinantal identities ⋮ Accurate Computations and Applications of Some Classes of Matrices ⋮ Total positivity and Neville elimination ⋮ Some generalized inverses of partition matrix and quotient identity of generalized Schur complement ⋮ Neville elimination: a study of the efficiency using checkerboard partitioning ⋮ Elimination techniques: From extrapolation to totally positive matrices and CAGD

Cites Work

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• Two composition methods for solving certain systems of linear equations
• A generalization of Sylvester's identity on determinants and some applications
• Generalized Schur-complements and a test for total positivity
• Schur complements and statistics
• Manifestations of the Schur complement