Balancing sparse matrices for computing eigenvalues

DOI10.1016/S0024-3795(00)00014-8zbMath0955.65025OpenAlexW2044756790MaRDI QIDQ1976919

James W. Demmel, Tzu-Yi Chen

Publication date: 14 February 2001

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

Full work available at URL: https://doi.org/10.1016/s0024-3795(00)00014-8

zbMATH Keywords

numerical examplessparse matrix algorithmcomputation of eigenvaluesbalancing algorithm: norm minimization

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15)

Related Items (7)

Balancing sparse Hamiltonian eigenproblems ⋮ Krylov--Schur-Type Restarts for the Two-Sided Arnoldi Method ⋮ Near-linear convergence of the random Osborne algorithm for matrix balancing ⋮ Palindromic quadratization and structure-preserving algorithm for palindromic matrix polynomials of even degree ⋮ Thick restarting the weighted harmonic Arnoldi algorithm for large interior eigenproblems ⋮ Estimating the condition number of \(f(A)b\) ⋮ Generalized self-concordant functions: a recipe for Newton-type methods

Uses Software

• LAPACK
• Harwell-Boeing sparse matrix collection

Cites Work

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• Balancing a matrix for calculation of eigenvalues and eigenvectors
• Minimization of norms and logarithmic norms by diagonal similarities
• Approximability by Weighted Norms of the Structured and VolumetricSingular Values of a Class of Nonnegative Matrices
• On Pre-Conditioning of Matrices
• Max-Balancing Weighted Directed Graphs and Matrix Scaling
• A Comparative Study of Algorithms for Matrix Balancing
• Line-sum-symmetric scalings of square nonnegative matrices
• Sparse matrix test problems
• An Implementation of Tarjan's Algorithm for the Block Triangularization of a Matrix
• Concerning Diagonal Similarity of Irreducible Matrices
• Matrix balancing
• Depth-First Search and Linear Graph Algorithms

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