Condition operators, condition numbers, and condition number theorem for the generalized eigenvalue problem

DOI10.1016/S0024-3795(96)00366-7zbMath0920.15001MaRDI QIDQ1368757

Jean-Pierre Dedieu

Publication date: 26 March 1998

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

zbMATH Keywords

generalized eigenvalue problemill-posed problemscondition numberscondition operators

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Conditioning of matrices (15A12)

Related Items (10)

A homogeneous Rayleigh quotient with applications in gradient methods ⋮ On condition numbers of a nondefective multiple eigenvalue of a nonsymmetric matrix pencil ⋮ Obituary: Jean-Pierre Dedieu, 1949-2012 ⋮ A comparison of eigenvalue condition numbers for matrix polynomials ⋮ The unavoidable condition\dots A report on the book. Book review of: P. Bürgisser and F. Cucker, Condition. The geometry of numerical algorithms ⋮ Kronecker's and Newton's approaches to solving: a first comparison ⋮ Multihomogeneous Newton methods ⋮ Conditioning and backward errors of eigenvalues of homogeneous matrix polynomials under Möbius transformations ⋮ Sensitivity Analysis of Nonlinear Eigenproblems ⋮ Perturbation theory for homogeneous polynomial eigenvalue problems

Cites Work

• On condition numbers and the distance to the nearest ill-posed problem
• It is possible to know a problem instance is ill-posed? Some foundations for a general theory of condition numbers
• Perturbation theorems for the generalized eigenvalue problem
• Complexity of Bezout’s Theorem IV: Probability of Success; Extensions
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