Guaranteed inclusions for the complex generalized eigenproblem

DOI10.1007/BF02239750zbMath0676.65028OpenAlexW1494163043MaRDI QIDQ1122940

Siegfried Michael Rump

Publication date: 1989

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02239750

zbMATH Keywords

random matricesinterval arithmeticgeneralized eigenvalue problemNewton methodPascal matricesinclusionHilbert matrices

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Interval and finite arithmetic (65G30) Inequalities involving eigenvalues and eigenvectors (15A42)

Related Items (11)

A proof via finite elements for Schiffer's conjecture on a regular pentagon ⋮ Fast enclosure for all eigenvalues in generalized eigenvalue problems ⋮ Verified eigenvalue and eigenvector computations using complex moments and the Rayleigh-Ritz procedure for generalized Hermitian eigenvalue problems ⋮ Unnamed Item ⋮ Verified solutions of delay eigenvalue problems ⋮ Determining the positive definiteness margin of interval matrices ⋮ A simple method for error bounds of eigenvalues of symmetric matrices ⋮ Determining the range of real eigenvalues for the interval generalized eigenvalue problem ⋮ Verified partial eigenvalue computations using contour integrals for Hermitian generalized eigenproblems ⋮ Numerical enclosure for each eigenvalue in generalized eigenvalue problem ⋮ Outer interval solution of the eigenvalue problem under general form parametric dependencies

Uses Software

• ACRITH-XSC

Cites Work

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• Automatic differentiation: techniques and applications
• Fehlerabschätzung reeller Eigenwerte und Eigenvektoren von Matrizen
• Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken
• The Arithmetic of the Digital Computer: A New Approach
• Overestimation in Linear Interval Equations

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