From Bareiss' algorithm to the stable computation of partial correlations

DOI10.1016/0377-0427(89)90361-0zbMath0681.65109OpenAlexW2118380063MaRDI QIDQ1823641

Ilse C. F. Ipsen, Jean-Marc Delosme

Publication date: 1989

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(89)90361-0

zbMATH Keywords

algorithmparallel computationCholesky factorizationLU factorizationGivens rotationshyperbolic rotationsdata flow graphhyperbolic Cholesky algorithmsample partial correlation coefficientsToeplitz coefficient matrix

Mathematics Subject Classification ID

Linear regression; mixed models (62J05) Parallel numerical computation (65Y05) Direct numerical methods for linear systems and matrix inversion (65F05) Probabilistic methods, stochastic differential equations (65C99)

Related Items (1)

On the \(QR\) algorithm and updating the \(SVD\) and the \(URV\) decomposition in parallel

Cites Work

• QR factorization of Toeplitz matrices
• Parallel solution of symmetric positive definite systems with hyperbolic rotations
• A method of matrix inverse triangular decomposition based on contiguous principal submatrices
• Generalized Schur complements
• An alternative Givens ordering
• Manifestations of the Schur complement
• Numerical solution of linear equations with Toeplitz and vector Toeplitz matrices
• A General Orthogonalization Technique with Applications to Time Series Analysis and Signal Processing
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