Computation of exact inertia and inclusions of eigenvalues (singular values) of tridiagonal (bidiagonal) matrices

DOI10.1016/j.laa.2006.09.008zbMath1118.65024OpenAlexW2151928524MaRDI QIDQ869919

N. E. Zubov

Publication date: 9 March 2007

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://ora.ox.ac.uk/objects/uuid:936b303a-59d1-4228-9e65-ed21a2b8b2b9

zbMATH Keywords

error analysisnumerical quadratureinterval arithmeticparallel algorithmsfactorizationbidiagonal matricesbisectionsymmetric tridiagonal matricesfloating point rounding modesGolub-Kahan formIEEE standardJacabi matricesLDL\(^{t}\) factorizationmonotonic arithmeticmultsection

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical solutions to overdetermined systems, pseudoinverses (65F20) Parallel numerical computation (65Y05)

Related Items (2)

$q$-Deformation of the Kac-Sylvester tridiagonal matrix ⋮ The eigenpairs of a Sylvester-Kac type matrix associated with a simple model for one-dimensional deposition and evaporation

Uses Software

• LAPACK
• ScaLAPACK

Cites Work

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• Accurate singular values and differential qd algorithms
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• On the correctness of some bisection-like parallel eigenvalue algorithms in floating point arithmetic
• More Accurate Bidiagonal Reduction for Computing the Singular Value Decomposition
• Interval arithmetic
• Accurate Singular Values of Bidiagonal Matrices
• Matrix Analysis
• LAPACK Users' Guide
• Accurately Counting Singular Values of Bidiagonal Matrices and Eigenvalues of Skew-Symmetric Tridiagonal Matrices
• Eigenvalues of tridiagonal symmetric interval matrices
• ScaLAPACK Users' Guide
• On Computing an Eigenvector of a Tridiagonal Matrix. Part I: Basic Results
• Computing Accurate Eigensystems of Scaled Diagonally Dominant Matrices
• Calculation of Gauss Quadrature Rules
• Calculating the Singular Values and Pseudo-Inverse of a Matrix
• [https://portal.mardi4nfdi.de/wiki/Publication:5727059 Tables for the Evaluation of � ∞ 0 x β e -x f(x) dx by Gauss-Laguerre Quadrature]

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