Solving nonlinear eigenvalue problems by algorithmic differentiation

DOI10.1007/BF02240067zbMath0582.65025OpenAlexW24191510MaRDI QIDQ1068512

Walter Gander, Peter Arbenz

Publication date: 1986

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02240067

zbMATH Keywords

numerical exampleseigenvaluesalgorithmic differentiationmatrix over complex functions

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical computation of determinants (65F40) Numerical differentiation (65D25) Matrices over function rings in one or more variables (15A54) Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17)

Related Items

Restricted rank modification of the symmetric eigenvalue problem: Theoretical considerations, Methods and algorithms of solving spectral problems for polynomial and rational matrices, The nonlinear eigenvalue problem, Robust generation of constrained B-spline curves based on automatic differentiation and fairness optimization, The generalized eigenvalue problem and acoustic surface wave computations, New algorithms for solving nonlinear eigenvalue problems, Large-scale complex eigenvalue problems, Numerical methods and questions in the organization of calculus. XII. Transl. from the Russian

Uses Software

• JAKEF
• Pascal-SC

Cites Work

• Automatic differentiation: techniques and applications
• A family of root finding methods
• A method for eigenvalues of sparse λ-matrices
• Differentiation in PASCAL-SC: type GRADIENT
• On Halley's Iteration Method
• Automatic Differentiation of Computer Programs
• $Ax = \lambda Bx$ and the Generalized Eigenproblem
• Algorithms for the Nonlinear Eigenvalue Problem
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