Stable polefinding and rational least-squares fitting via eigenvalues

DOI10.1007/s00211-018-0948-4zbMath1391.65033OpenAlexW2791830176WikidataQ55398224 ScholiaQ55398224MaRDI QIDQ1651007

Yuji Nakatsukasa, Shinji Ito

Publication date: 16 July 2018

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-018-0948-4

Mathematics Subject Classification ID

Numerical interpolation (65D05) Algorithms for approximation of functions (65D15)

Related Items (2)

Efficient Reduction of Compressed Unitary Plus Low Rank Matrices to Hessenberg Form ⋮ The AAA Algorithm for Rational Approximation

Uses Software

• Matlab
• FEAST
• mctoolbox
• Chebfun
• AAA

Cites Work

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• Matrices for the direct determination of the barycentric weights of rational interpolation
• A derivative-free algorithm for computing zeros of analytic functions
• The convergence of Padé approximants to functions with branch points
• A projection method for generalized eigenvalue problems using numerical integration.
• The eigenstructure of an arbitrary polynomial matrix: Computational aspects
• On locating clusters of zeros of analytic functions
• Backward error and condition of polynomial eigenvalue problems
• Computing the zeros of analytic functions
• Robust rational interpolation and least-squares
• Condition numbers and equilibration of matrices
• An Algorithm for the Generalized Eigenvalue Problem for Nonsquare Matrix Pencils by Minimal Perturbation Approach
• On the stability of computing polynomial roots via confederate linearizations
• Fast and Stable Rational Interpolation in Roots of Unity and Chebyshev Points
• Numerical Algorithms Based on Analytic Function Values at Roots of Unity
• The Exponentially Convergent Trapezoidal Rule
• Non-asymptotic theory of random matrices: extreme singular values
• THE COLLEAGUE MATRIX, A CHEBYSHEV ANALOGUE OF THE COMPANION MATRIX
• Some New Aspects of Rational Interpolation
• On the Scalar Rational Interpolation Problem
• Spectral Methods in MATLAB
• Barycentric Lagrange Interpolation
• An Extension of MATLAB to Continuous Functions and Operators
• The Condition Number of Equivalence Transformations That Block Diagonalize Matrix Pencils
• Accuracy and Stability of Numerical Algorithms
• Robust Padé Approximation via SVD
• Computing Eigenvalues of Real Symmetric Matrices with Rational Filters in Real Arithmetic
• Generalized Rational Krylov Decompositions with an Application to Rational Approximation
• The RKFIT Algorithm for Nonlinear Rational Approximation
• A Numerical Method for Locating the Zeros of an Analytic Function
• An Algorithm for Generalized Matrix Eigenvalue Problems

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