An algorithm for computing Jordan chains and inverting analytic matrix functions

DOI10.1016/j.laa.2007.06.012zbMath1132.47010OpenAlexW1974370014MaRDI QIDQ2383013

Jon Wilkening

Publication date: 5 October 2007

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

Full work available at URL: https://doi.org/10.1016/j.laa.2007.06.012

zbMATH Keywords

Laurent seriesmatrix inversionmatrix-valued functionKeldysh chainanalytic perturbationJordan chainanalytic matrix functionsolution of linear constant coefficient ODE

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Explicit solutions, first integrals of ordinary differential equations (34A05) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Canonical forms, reductions, classification (15A21) Matrix pencils (15A22) Chains (nests) of projections or of invariant subspaces, integrals along chains, etc. (47A46)

Related Items (15)

Accurate spectral numerical schemes for kinetic equations with energy diffusion ⋮ Some results on eigenvalues of finite type, resolvents and Riesz projections ⋮ A local construction of the Smith normal form of a matrix polynomial ⋮ The fundamental equations for the generalized resolvent of an elementary pencil in a unital Banach algebra ⋮ Spatially quasi-periodic bifurcations from periodic traveling water waves and a method for detecting bifurcations using signed singular values ⋮ Inversion of regular analytic matrix functions: Local Smith form and subspace duality ⋮ Continuation of eigenvalues and invariant pairs for parameterized nonlinear eigenvalue problems ⋮ Closed form solution for the equations of motion for constrained linear mechanical systems and generalizations: an algebraic approach ⋮ The fundamental equations for inversion of operator pencils on Banach space ⋮ Computation of time-periodic solutions of the Benjamin-Ono equation ⋮ Inverting a Matrix Function around a Singularity via Local Rank Factorization ⋮ INVERSION OF OPERATOR PENCILS ON HILBERT SPACE ⋮ Harmonic stability of standing water waves ⋮ Inversion of operator pencils on Banach space using Jordan chains when the generalized resolvent has an isolated essential singularity ⋮ An Explicit Formula for the Splitting of Multiple Eigenvalues for Nonlinear Eigenvalue Problems and Connections with the Linearization for the Delay Eigenvalue Problem

Cites Work

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• Construction of Corner Singularities for Agmon-Douglis-Nirenberg Elliptic Systems
• A Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part I: Versal Deformations
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