Diagonal Scalings for the Eigenstructure of Arbitrary Pencils

DOI10.1137/20M1364011zbMath1498.15018arXiv2009.00482OpenAlexW3082583660MaRDI QIDQ5094219

Paul Van Dooren, María C. Quintana, Froilán M. Dopico

Publication date: 2 August 2022

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.00482

zbMATH Keywords

regularizationeigenvaluesdiagonal scalingpencilsSinkhorn-Knopp algorithm

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Ill-posedness and regularization problems in numerical linear algebra (65F22) Eigenvalues, singular values, and eigenvectors (15A18) Numerical computation of matrix norms, conditioning, scaling (65F35) Matrix pencils (15A22)

Uses Software

• LAPACK
• Matlab

Cites Work

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• Computational Optimal Transport: With Applications to Data Science
• The computation of Kronecker's canonical form of a singular pencil
• Scalings of matrices which have prespecified row sums and column sums via optimization
• Matrices of 0's and 1's with total support
• The chainable matrix, a special combinatorial matrix
• Concerning nonnegative matrices and doubly stochastic matrices
• The spectrum of a nonlinear operator associated with a matrix
• Balancing a matrix for calculation of eigenvalues and eigenvectors
• The Sinkhorn–Knopp Algorithm: Convergence and Applications
• LAPACK Users' Guide
• Balancing the Generalized Eigenvalue Problem
• Properties of Kruithof's Projection Method
• Balancing Regular Matrix Pencils
• Convex Sets of Non-Negative Matrices
• Matrix Links, An Extremization Problem, and the Reduction of a Non-Negative Matrix to One With Prescribed Row and Column Sums
• An Algorithm for Generalized Matrix Eigenvalue Problems