On the fast Lanczos method for computation of eigenvalues of Hankel matrices using multiprecision arithmetics

DOI10.1002/nla.2035zbMath1413.65089OpenAlexW2269503043MaRDI QIDQ2829108

Shaun Bangay, Gleb Beliakov

Publication date: 26 October 2016

Published in: Numerical Linear Algebra with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/nla.2035

zbMATH Keywords

eigenvalueLanczos methodToeplitz matrixHankel matrixmultiprecision arithmetics

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical methods for discrete and fast Fourier transforms (65T50) Toeplitz, Cauchy, and related matrices (15B05)

Uses Software

• FLINT
• gmp
• MPFR
• JDQR
• ARPACK
• Kiss FFT
• JDQZ
• advanpix
• ARPREC
• MPC
• Arb

Cites Work

• A fast eigenvalue algorithm for Pascal matrices
• The Riemann hypothesis. A resource for the afficionado and virtuoso alike
• Analysis of the symmetric Lanczos algorithm with reorthogonalization methods
• A fast eigenvalue algorithm for Hankel matrices
• Fast algorithms for Toeplitz and Hankel matrices
• Numerical Methods for Large Eigenvalue Problems
• The Lanczos Algorithm With Partial Reorthogonalization
• MPFR
• A Divide-and-Conquer Algorithm for the Symmetric Tridiagonal Eigenproblem
• Templates for the Solution of Algebraic Eigenvalue Problems
• Approximation of Riemann’s Zeta Function by Finite Dirichlet Series: A Multiprecision Numerical Approach

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