The eigenvalue problem for infinite complex symmetric tridiagonal matrices with application

DOI10.1016/0024-3795(95)00699-0zbMath0857.15001OpenAlexW2004556758MaRDI QIDQ1923165

Yasuhiko Ikebe, Dengsheng Cai, Nobuyoshi Asai, Yoshinori Miyazaki

Publication date: 11 March 1997

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

Full work available at URL: https://doi.org/10.1016/0024-3795(95)00699-0

zbMATH Keywords

Mathieu equationeigenvalueseigenvectoreigenvalue approximationcomplex symmetric tridiagonal matrices

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60)

Related Items (11)

Discrete spectra for some complex infinite band matrices ⋮ On the common zeros of Bessel functions ⋮ On the similarity of complex symmetric operators to perturbations of restrictions of normal operators ⋮ The characteristic function for Jacobi matrices with applications ⋮ Semi-analytical Karhunen-Loeve representation of irregular waves based on the prolate spheroidal wave functions ⋮ On the non-self-adjoint and multiscale character of passive scalar mixing under laminar advection ⋮ Mathieu functions for purely imaginary parameters ⋮ Asymptotics of eigenvalues of infinite block matrices ⋮ The Mathieu differential equation and generalizations to infinite fractafolds ⋮ Computation of multiple eigenvalues of infinite tridiagonal matrices ⋮ Eigenvalue problems for a class of infinite complex symmetric tridiagonal matrices with related three-term recurrence relation

Uses Software

• LAPACK
• EISPACK

Cites Work

• Eigenvalues for infinite matrices
• Non-overlapping partitions, continued fractions, Bessel functions and a divergent series
• Matrix eigensystem routines - EISPACK guide. 2nd ed
• The eigenvalue problem for infinite compact complex symmetric matrices with application to the numerical computation of complex zeros of \(J_ 0(z)- iJ_ 1(z)\) and of Bessel functions \(J_ m(z)\) of any real order \(m\)
• On Bessel Functions and Rate of Convergence of Zeros of Lommel Polynomials
• Computational Aspects of Three-Term Recurrence Relations
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