Spectra of Jacobi operators via connection coefficient matrices

DOI10.1007/s00220-021-03939-wOpenAlexW3130394477MaRDI QIDQ2662845

Marcus Webb, Sheehan Olver

Publication date: 15 April 2021

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.03095

zbMATH Keywords

orthogonal polynomialstridiagonal matrixJacobi operatorconnection matrixperturbed Toeplitz operatorSolvability Complexity Index

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Numerical interpolation (65D05) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36) Applications of operator theory in numerical analysis (47N40) Applications of functional analysis in numerical analysis (46N40)

Related Items (12)

Large deviations for spectral measures of some spiked matrices ⋮ A contour method for time-fractional PDEs and an application to fractional viscoelastic beam equations ⋮ The foundations of spectral computations via the solvability complexity index hierarchy ⋮ Computing eigenvalues of semi-infinite quasi-Toeplitz matrices ⋮ The mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systems ⋮ An inequality for imaginary parts of eigenvalues of non-compact operators with Hilbert-Schmidt Hermitian components ⋮ Computing Semigroups with Error Control ⋮ Variations of real and imaginary parts of eigenvalues of compact operators under perturbations ⋮ Stability of the Lanczos algorithm on matrices with regular spectral distributions ⋮ On the complexity of the inverse Sturm-Liouville problem ⋮ Computing spectral measures and spectral types ⋮ Computing Spectral Measures of Self-Adjoint Operators

Uses Software

• DLMF
• Chebfun
• OPQ
• ApproxFun
• GitHub
• SpectralMeasures.jl
• ValidatedNumerics.jl
• ComplexPhasePortrait.jl

Cites Work

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• ValidatedNumerics.jl
• ComplexPhasePortrait.jl
• Infinite random matrix theory, tridiagonal bordered Toeplitz matrices, and the moment problem
• Compact perturbations of orthogonal polynomials
• New barriers in complexity theory: on the solvability complexity index and the towers of algorithms
• Sum rules via large deviations
• Asymptotics for orthogonal polynomials with regularly varying recurrence coefficients
• Perturbations of orthogonal polynomials with periodic recursion coefficients
• On the calculation of Jacobi matrices
• Orthogonal polynomials with asymptotically periodic recurrent coefficients
• Orthogonal polynomials, associated polynomials and functions of the second kind
• Modified moments and Gaussian quadratures
• Sum rules for Jacobi matrices and their applications to spectral theory
• Perturbation theory for linear operators.
• Jost functions and Jost solutions for Jacobi matrices. I: A necessary and sufficient condition for Szegő asymptotics
• An algorithm for Gaussian quadrature given modified moments
• On the Solvability Complexity Index, the 𝑛-pseudospectrum and approximations of spectra of operators
• Visual Complex Functions
• The Analytic Theory of Matrix Orthogonal Polynomials
• Jost functions and Jost solutions for Jacobi matrices, II. Decay and analyticity
• Some open problems in random matrix theory and the theory of integrable systems
• Orthogonal Polynomials, Measures and Recurrence Relations
• Scattering Theory and Polynomials Orthogonal on the Real Line
• Orthogonal polynomials
• Fast and Backward Stable Computation of Roots of Polynomials
• Theoretical Numerical Analysis
• On the Construction of Gaussian Quadrature Rules from Modified Moments
• The connection between systems of polynomials orthogonal with respect to different distribution functions
• How to find all roots of complex polynomials by Newton's method.

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