Continuation of Invariant Subspaces for Parameterized Quadratic Eigenvalue Problems

DOI10.1137/080723107zbMath1201.65050OpenAlexW2088810629MaRDI QIDQ3584164

V. Thümmler, Wolf-Jürgen Beyn

Publication date: 19 August 2010

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

Full work available at URL: https://semanticscholar.org/paper/9f4300a4d442a711f7e75b930c88043b02439af6

zbMATH Keywords

Newton's methodnumerical examplespredictor-corrector methodsparse matricesnumerical continuationBartels-Stewart algorithmquadratic eigenvalue problembifurcation problems

Mathematics Subject Classification ID

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

Related Items (13)

A block Newton method for nonlinear eigenvalue problems ⋮ Block Newton method and block Rayleigh quotient iteration for computing invariant subspaces of general complex matrices ⋮ Eigenvalue embedding problem for quadratic regular matrix polynomials with symmetry structures ⋮ The nonlinear eigenvalue problem ⋮ Continuation of eigenvalues and invariant pairs for parameterized nonlinear eigenvalue problems ⋮ Path-following methods for calculating linear surface wave dispersion relations on vertical shear flows ⋮ Broyden's Method for Nonlinear Eigenproblems ⋮ Path-Following Method to Determine the Field of Values of a Matrix with High Accuracy ⋮ Efficient and reliable hp-FEM estimates for quadratic eigenvalue problems and photonic crystal applications ⋮ Perturbation, extraction and refinement of invariant pairs for matrix polynomials ⋮ Möbius transformations of matrix polynomials ⋮ Memory-efficient Arnoldi algorithms for linearizations of matrix polynomials in Chebyshev basis ⋮ A contour integral approach to the computation of invariant pairs

Uses Software

• MATCONT
• NLEVP
• NewtonLib

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