Pivot tightening for direct methods for solving symmetric positive definite systems of linear interval equations

DOI10.1007/S00607-011-0159-7zbMath1238.65019OpenAlexW2002877864MaRDI QIDQ411425

Jürgen Garloff

Publication date: 4 April 2012

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00607-011-0159-7

zbMATH Keywords

algorithmnumerical exampleslinear interval equationsdirect methodsinterval Cholesky methodpositive definite interval matrixToeplitz system

Mathematics Subject Classification ID

Interval and finite arithmetic (65G30) Direct numerical methods for linear systems and matrix inversion (65F05) Algorithms with automatic result verification (65G20)

Uses Software

• INTLAB

Cites Work

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• Intervals of P-matrices and related matrices
• On some properties of positive definite Toeplitz matrices and their possible applications
• The Cholesky method for interval data
• Monotone convex sequences and Cholesky decomposition of symmetric Toeplitz matrices
• Numerical solution of linear equations with Toeplitz and vector Toeplitz matrices
• Lower bounds of the minimal eigenvalue of a Hermitian positive-definite matrix
• Bounds on Real Eigenvalues and Singular Values of Interval Matrices
• New Criteria for the Feasibility of the Cholesky Method with Interval Data
• Interval Gaussian Elimination with Pivot Tightening
• Bounds on the extreme eigenvalues of positive-definite Toeplitz matrices
• Inverse Interval Matrix
• Bounds on Eigenvalues of Interval Matrices
• Positive Definiteness and Stability of Interval Matrices
• The Solution of a Toeplitz Set of Linear Equations
• On lower bounds for the smallest eigenvalue of a Hermitian positive-definite matrix
• An Algorithm for the Inversion of Finite Toeplitz Matrices

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